Clinton was hastily dispatched to the region by President Barack Obama to join a high-profile group of world leaders working to halt the violence. Standing alongside the Israeli leader, Clinton indicated it could take some time to iron out an agreement.
"In the days ahead, the United States will work with our partners here in Israel and across the region toward an outcome that bolsters security for the people of Israel, improves conditions for the people of Gaza and moves toward a comprehensive peace for all people of the region," she said.
Clinton expressed sorrow for the heavy loss of life on both sides, but called for the Palestinian rocket attacks on Israel to end and stressed that the American commitment to Israel's security is "rock solid."
"The goal must be a durable outcome that promotes regional stability and advances the security and legitimate aspirations of Israelis and Palestinians alike," she said.
In Washington, State Department spokeswoman Victoria Nuland said Clinton met with Netanyahu and other Israeli officials for two hours.
"They discussed efforts to de-escalate the situation and bring about a sustainable outcome that protests Israel's security and improves the lives of civilians in Gaza," Nuland said. "They also consulted on her impending stops in Ramallah and Cairo, including Egyptian efforts to advance de-escalation."
Israel launched the offensive on Nov. 14 in a bid to end months of rocket attacks out of the Hamas-run territory, which lies on Israel's southern flank. After assassinating Hamas' military chief, it has carried out a blistering campaign of airstrikes, targeting rocket launchers, storage sites and wanted militants.
The campaign has killed more than 130 Palestinians, including dozens of civilians, and wounded hundreds of others. Five Israelis have been killed by rocket fire, including a soldier and a civilian contractor on Tuesday.
With Israel massing thousands of ground troops on the Gaza border, diplomats raced throughout the region in search of a formula to halt the fighting.
In a meeting with Netanyahu, U.N. chief Ban Ki-moon condemned Palestinian rocket attacks, but urged Israel to show "maximum restraint."
"Further escalation benefits no one," he said.
Israel demands an end to rocket fire from Gaza and a halt to weapons smuggling into Gaza through tunnels under the border with Egypt. It also wants international guarantees that Hamas will not rearm or use Egypt's Sinai region, which abuts both Gaza and southern Israel, to attack Israelis.
Hamas wants Israel to halt all attacks on Gaza and lift tight restrictions on trade and movement in and out of the territory that have been in place since Hamas seized Gaza by force in 2007. Israel has rejected such demands in the past.
Egypt's new Islamist government is expected to play a key role in maintaining a deal.
The crisis has thrust Egypt's president, Mohammed Morsi, into the spotlight as he plays a difficult balancing act.
Morsi belongs to the Muslim Brotherhood, Hamas' parent movement, and clearly sympathizes with the Islamic militant group. At the same time, he relies heavily on U.S. aid and is trying to preserve a historic peace agreement with Israel.
Earlier, Morsi raised hopes that a cease-fire was near when he predicted the negotiations would yield "positive results" during the coming hours.
Netanyahu also said his country would be a "willing partner" in a cease-fire agreement.
But as the talks stretched into the evening, it became clear that a deal remained a ways off.
"Most likely the deal will be struck tomorrow. Israel has not responded to some demands, which delayed the deal," Hamas official Izzat Risheq said.
Hamas officials refused to discuss the remaining sticking points.
Israeli media quoted Defense Minister Ehud Barak as telling a closed meeting that Israel wanted a 24-hour test period of no rocket fire to see if Hamas could enforce a truce.
Palestinian officials briefed on the negotiations said Hamas wanted assurances of a comprehensive deal that included new border arrangements and were resisting Israeli proposals for a phased agreement. The officials spoke on condition of anonymity because they were not authorized to talk to the media.
Although Israel claims it has inflicted heavy damage on militants' capabilities, its roughly 1,550 airstrikes and shelling attacks have failed to halt the rocket fire.
More than 1,400 rockets have been fired at Israel, including about 200 on Tuesday. A U.S.-financed Israeli rocket-defense system has knocked down roughly 400 of the incoming projectiles.
Violence raged on as the talks continued. An airstrike late Tuesday killed two journalists who work for the Hamas TV station, Al-Aqsa, according to a statement from the channel. A third journalist, from Al Quds Educational Radio, a private station, also was killed.
The Al-Aqsa TV cameramen were in a car hit by an airstrike, Gaza health official Ashraf al-Kidra said. Israel claims that many Hamas journalists are involved in militant activities. Earlier this week it targeted the station's offices, saying they served as a Hamas communications post.
Late Tuesday, a Palestinian rocket hit a house in the central Israeli city of Rishon Lezion, wounding two people and badly damaging the top two floors of the building, police spokesman Micky Rosenfeld said.
Minutes before Ban's arrival in Jerusalem from Egypt, Palestinian militants fired a rocket toward Jerusalem, just the second time it has targeted the city. The rocket fell in an open area southeast of the city.
Jerusalem had previously been considered beyond the range of Gaza rockets and an unlikely target because it is home to the Al-Aqsa Mosque compound, Islam's third-holiest shrine.
Israeli warplanes dropped leaflets on several Gaza neighborhoods asking residents to evacuate and head toward the center of Gaza City along specific roads. The army "is not targeting any of you, and doesn't want to harm you or your families," the leaflets said. Palestinian militants urged residents to ignore the warnings, calling them "psychological warfare."
Israeli security officials acknowledge they rely on a network of Palestinian informants to identify targets. Masked gunmen publicly shot dead six suspected collaborators with Israel in a large Gaza City intersection Tuesday, witnesses said.
An Associated Press reporter saw a mob surrounding five of the bloodied corpses shortly after the killing, and one of the bodies was dragged through the streets by a motorcycle.
Hamas did not provide any evidence against the alleged collaborators.
Clinton was also scheduled to meet with Palestinian President Mahmoud Abbas in the West Bank and Egyptian leaders in Cairo on Wednesday. Turkey's foreign minister and a delegation of Arab League foreign ministers traveled to Gaza on a separate truce mission. Airstrikes continued to hit Gaza even as they entered the territory.
"Turkey is standing by you," Turkish Foreign Minister Ahmet Davutoglu told the Hamas prime minister in Gaza, Ismail Haniyeh. "Our demand is clear. Israel should end its aggression immediately and lift the inhumane blockade imposed on Gaza."
The U.S. considers Hamas, which has killed hundreds of Israelis in suicide and other attacks, to be a terror group and does not meet with its officials. The Obama administration blames Hamas for the latest eruption of violence and says Israel has the right to defend itself. At the same time, it has warned against a ground invasion, saying it could send casualties spiraling.
Obama speaks to Egyptian president on Gaza crisis
YOKOTA AIR BASE, Japan • The White House says President Barack Obama has again spoken to Egyptian President Mohammed Morsi as he seeks to end nearly a week of warfare between Israel and Hamas.
Obama spoke to Morsi for the third time in 24 hours as he was returning home Tuesday from a diplomatic tour of Asia. Deputy National Security adviser Benjamin Rhodes said Obama wanted to talk to Morsi before Secretary of State Hillary Rodham Clinton's expected arrival in Israel to underscore the importance of working to halt the violence.
Rhodes said Obama commended Morsi's efforts to ease tensions and stressed the important role Egypt can play in regional security.
Rhodes said Obama believes a diplomatic solution is urgently needed, but he emphasized that Hamas must stop firing rockets from Gaza into Israel.