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