Updated at 4:50 p.m. ET: Following her arrival in Israel, Secretary of State Hillary Clinton reiterated at a press conference Tuesday that America's commitment to Israel's security is "rock solid," adding that "the goal must be a durable outcome that promotes regional stability and advances the security and legitimate aspirations of Israelis and Palestinians alike."

"The rocket attacks from terrorist organizations inside Gaza on Israeli cities and towns must end, and a broader calm restored," Clinton said, adding that there are no substitutes for security and a just and lasting peace.

Speaking in Jerusalem, Clinton also offered her condolences for those lost in the violence.

"Our hearts break for the loss of every civilian, Israeli and Palestinian, and for all those who have been wounded and are living in fear and danger," she said, adding that she would work with Israel and Egypt on brokering a truce in Gaza "in the days ahead."

Israel is prepared to escalate its offensive but would prefer a long-term diplomatic solution, Prime Minister Benjamin Netanyahu said on Tuesday.

"If there is a possibility of achieving a long-term solution to this problem with diplomatic means, we prefer that," he said in a public statement alongside Clinton.

"But if not, I'm sure you understand that Israel will have to take whatever action is necessary to defend its people."

Earlier, a Hamas official said a truce with Israel would not be reached Tuesday because the Israeli government had yet to respond to proposals.

"The Israeli side has not responded yet, so we will not hold a (news) conference this evening and must wait until tomorrow," Ezzat al-Rishq, a senior Hamas leader, told Reuters. "The truce is now held up because we are waiting for the Israeli side to respond," he added in a short telephone interview.

Clinton landed at 9:51 p.m. local time in Tel Aviv, where she met with Netanyahu. Later, Clinton will meet with the President of the Palestinian National Authority Mahmoud Abbas in Ramallah before heading to Cairo.

A U.S. official stressed to NBC News that Clinton would not meet with representatives of Hamas, the Islamist organization that controls the Gaza Strip, largely because of its failure to renounce terrorism and recognize Israel's right to exist.

Egyptian officials said talks are ongoing to reach a truce in Gaza, although any agreement appears unlikely to address the long-term areas of disagreement between Israel and the Hamas leaders of the Gaza Strip, NBC's Ayman Mohyeldin reported Tuesday.

The expected "cessation of hostilities" will call on all parties to use maximum restraint, according to one former intelligence official familiar with the talks.

Slideshow: Israel, Gaza violence escalates

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Two sides exchange deadly airstrikes, rocket attacks.

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Earlier Tuesday, President Barack Obama spoke to Egyptian President Mohammed Morsi, who is seeking to broker a cease-fire between Israel and Hamas. 

According to White House officials, Obama spoke to Morsi for the third time in 24 hours. Deputy National Security adviser Ben Rhodes said Obama wanted to talk to Morsi before Clinton's arrival in Israel.

Rhodes said Obama underscored the importance of Morsi working toward a de-escalation to the conflict in Gaza. He also commended Morsi's efforts to pursue a de-escalation and acknowledged Egypt's important role in the region's security.

Rhodes said Obama emphasized the importance of a diplomatic solution, but said that rocket fire from Gaza into Israel must stop.

Israel Defense Forces continued airstrikes overnight, and also said 39 rockets fired from Gaza hit Israel Tuesday in a message on its Twitter account.

Since Israel launched its military campaign seven days ago in response to rocket fire, more than 100 people in Gaza and three people in Israel have been killed.

Internationally, the main focus was on stopping the violence, and Morsi hinted at a possible breakthrough Tuesday.

Speaking at his sister's funeral in Egypt, Morsi said the "aggression on Gaza" would end Tuesday. He made the apparently off-the-cuff comments in front of mourners who had come to pay their respects, but did not elaborate. Several journalists traveling with Morsi confirmed he made the remark.

'Army must invade': In southern Israel, support grows for action in Gaza

In Jerusalem, Netanyahu said Israel would be a “willing partner” in a cease-fire, but also issued a warning.

He said if further military action proved necessary “to stop the constant barrage of rockets, Israel will not hesitate to do what is necessary to defend our people.”

And Mohammed Deif, the new leader of Hamas' military wing, sounded a defiant note, saying that the movement was ready to fight and would not back down from its efforts to liberate Palestine.

He was speaking in his first audio recording since the group’s previous top military commander, Ahmed Jabari, was killed in an Israeli airstrike Wednesday. Deif, who has survived several assassination attempts in the past, called for Hamas’ supporters to remain steadfast. 

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'Difficult' situation

It is unclear how much influence Clinton can have on the situation.

“She is going to go out there to be in the region to have direct, face-to-face discussions with those leaders,” Rhodes said. “I don’t want to predict exactly what the outcome of those discussions will be. We all know how difficult this situation is.” 

The White House thinks the leaders who are heavily involved in the region “understand what the best outcome is,” Rhodes added, but that a peaceful goal is only achievable “if Hamas takes action to stop what they’ve been doing.”

An Israeli soldier and a civilian died when rockets exploded near the Gaza frontier, police and the army said.

An Israeli air strike on two cars in the Gaza Strip killed six Palestinians Tuesday, while two children died in an attack in the north of the territory, local residents and medics told Reuters. 

United Nations Secretary-General Ban Ki-moon called Tuesday for an immediate cease-fire in Gaza and said a threatened Israeli ground operation in the Palestinian enclave would be a “dangerous escalation” that must be avoided.

Later, standing alongside Netanyahu in Jerusalem, Ban urged Israel to show "maximum restraint" and condemned rocket attacks on Israel.

Also Tuesday, Arab League chief Nabil Elaraby and the foreign ministers of Turkey, Egypt, Lebanon, Tunisia and Sudan traveled from Egypt to Gaza in an unprecedented move designed to show solidarity with the Palestinians, NBC News reported.

US Embassy guard wounded
Meanwhile, a man was arrested after he stabbed a security guard Tuesday at the U.S. Embassy in Tel Aviv, a police spokesman told Reuters. 

The spokesman said the guard opened fire during the attack.

Israel Radio said the attacker, who police said was armed with a knife and an ax, was wounded. 

Oded Balilty / AP

Israeli police officers detain a man who attacked a security guard at the U.S. embassy in Tel Aviv, Israel, Tuesday.

NBC's Shawna Thomas, Ayman Mohyeldin and Ian Johnston, and Reuters contributed to this report.

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SANA via AFP - Getty Images

A handout picture released Tuesday by the official Syrian Arab News Agency shows Syrian President Bashar Assad, right, meeting with Saeed Jalili, a top aide to Iran's supreme leader Ayatollah Ali Khamenei, in Damascus.

Updated at 8:31 p.m. ET: As Syrian President Bashar Assad appeared on television for the first time in two weeks on Tuesday, U.S. Secretary of State Hillary Clinton said that the high-profile defection of the Syrian prime minister increased the urgency of planning for the ouster of Assad's regime.

In South Africa's capital, Pretoria, Clinton said the United States and other countries needed to make sure that Syrian state institutions remain intact once Assad loses his grip on power.

"The intensity of the fighting in Aleppo, the defections, really point out how imperative it is that we come together and work toward a good transition plan," Clinton said.

"I do think we can begin talking about planning for what happens next: the day after the regime does fall. I am not going to put a timeline on it, I can't possibly predict it, but I know it's going to happen as do most observers around the world," Clinton said.

Clinton also warned against "proxies or terrorist fighters" being sent in to join the 17-month-old conflict.

The escalating war in Syria has increasingly divided the region along its sectarian faultline, pitting the mainly-Sunni rebels, who are backed by regional Sunni-led powers Turkey and the Gulf Arab states, against Assad's government that is backed by Shiite Iran.

In a possible sign of increasing American pressure on Assad’s government, Clinton's remarks come a day after three U.S. senators warned about the risks of American failure to provide assistance to Syrian opposition fighters.

Clinton also spoke a day after the defection of Prime Minister Riyad Hijab, the latest in a string of high-level departures from the Assad regime.

US makes plans to keep post-Assad Syria intact

TV appearance
Assad appeared on Syrian state TV on Tuesday meeting with Iran's Supreme National Security Council in Damascus.

Assad's absence had fueled rumors about his health, including a hoax Twitter message Monday that quoted Russia's ambassador to Damascus as saying Assad might have been killed.

Russian officials quickly denied the report.

Three US senators warn about risks of inaction in Syria

In the week after a July 18 bombing that killed four members of his inner circle, Assad was shown twice in silent footage on television, swearing in a new defense minister and meeting military officials.

Slideshow: The lives of Syrian rebels

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People resisting the army of President Bashar Assad in northern Syria cope with loss and prepare for fighting.

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During Tuesday's Damascus meeting, Saeed Jalili, head of Iran's Supreme National Security Council, said Iran would not let its close partnership with the Syrian leadership to be shaken by the uprising or external foes.

"Iran will not allow the axis of resistance, of which it considers Syria to be an essential part, to be broken in any way," Syrian television quoted Jalili as saying.

The "axis of resistance" refers to Shiite Iran's anti-Israel alliance with Syria's rulers - from the Alawite faith which is an offshoot of Shiite Islam - and the Lebanese Shiite militant group Hezbollah, which fought a month-long war with Israel in 2006, with Iranian and Syrian support. 

Damascus and Tehran have held Sunni Muslim Gulf Arab states and Turkey, all allies of the United States and European powers, responsible for the bloodshed in Syria by supporting the overwhelmingly Sunni Muslim rebels. Western powers sympathetic to the rebels are concerned that anti-Western Sunni Islamists could benefit from a victory for the anti-Assad forces. 

Iran's Fars news agency said Jalili told Assad that Iran was prepared to provide humanitarian aid to Syria. 

As estimated 18,000 people have been killed in the Syrian conflict, as rebels battle government forces in an attempt to wrest control from the Assad family's four-decade grip on power.

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On a fence-mending visit to Turkey, Iranian Foreign Minister Ali Akbar Salehi said he wanted to work with Ankara to resolve the crisis. Turkish Prime Minister Tayyip Erdogan described as "worrying" a comment on Monday by Tehran's top general, who blamed Turkey, Saudi Arabia and Qatar for bloodshed in Syria. 

Iran has expressed fears for more than 40 Iranians it says are religious pilgrims kidnapped by rebels from a bus in Damascus while visiting Shiite shrines. Salehi wrote to U.N. Secretary-General Ban Ki-moon seeking his help to free them. 

Rebels say they suspect the captives were troops sent to help Assad. A rebel spokesman in the Damascus area said on Monday three of the Iranians had been killed by government shelling. He initially said the rest would be executed if the shelling did not stop but later said they were being questioned. 

Fighting rages in Aleppo
On Tuesday, rebels trying to fight off an army offensive in Aleppo said they were running low on ammunition as government forces encircled their stronghold at the southern entrance to the country's biggest city.

Assad has reinforced his troops in preparation for an assault to recapture rebel-held districts of Aleppo after repelling fighters from most of Damascus.

Related: Official: Syria PM defects to anti-Assad opposition

"The Syrian army is trying to encircle us from two sides of Salaheddine," said Sheikh Tawfiq, one of the rebel commanders, referring to the southwestern neighborhood which has seen heavy fighting over the last week.

Mortar fire and tank shells exploded across the district early Tuesday, forcing rebel fighters to take cover in crumbling buildings and rubble-strewn alleyways.

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Tanks have entered parts of Salaheddine and army snipers, using the cover of heavy bombardment, deployed on rooftops, hindering rebel movements.

Slideshow: Behind Syrian rebel lines

Machine guns operated by motorcycle brakes? Get a glimpse at the rebels fighting against Assad's forces in Syria's mountainous Jabal al-Zawiya area.

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Another rebel commander, Abu Ali, said snipers at the main Saleheddine roundabout were preventing the rebels from bringing in reinforcements and supplies. He said five of his fighters were killed on Monday and 20 wounded.

But rebels said they were still holding the main streets of Salaheddine which have been the frontline of their clashes with Assad's forces.

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A fighter jet pounded targets in the eastern districts of Aleppo and artillery shelling could be heard in the early morning, an activist in Aleppo said.

"Two families, about 14 people in total, were believed killed when a shell hit their home and it collapsed this morning," the activist said. The house was one street away from a school being used by rebels, he said.

Reuters, The Associated Press and NBC News' staff contributed to this report.

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