Updated at 5:06 p.m. ET
With U.S. Secretary of State Hillary Rodham Clinton by his side, Israeli Prime Minister Benjamin Netanyahu said Tuesday that he preferred a diplomatic solution to the conflict between his country and Hamas militants, but also said that Israel would "take whatever action is necessary to protect its people."
Clinton said the United States was pushing for "durable outcome" to end the violence in the Gaza Strip.
"In the days ahead, the United States will work with our partners here in Israel and across the region toward an outcome the 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," Clinton said.
She met with Netanyahu after a diplomatic push to end Israel's nearly weeklong offensive was put on hold when a top adviser to Egypt's president said that an expected cease-fire announcement would not happen Tuesday, CBS News correspondent Clarissa Ward reports from Cairo.
The unnamed adviser to Egyptian President Mohammed Morsi had said Morsi would announce the cease-fire Tuesday night in Cairo, where cease-fire talks were being held. Nearly an hour after the expected time of the announcement, the adviser said it wasn't going to happen Tuesday night, Ward reports.
A spokesperson for Morsi's party, the political wing of the Muslim Brotherhood in Egypt, later said that the delay was because of an Israeli request to postpone the announcement until Wednesday, Ward reports.
Earlier Tuesday, a source close to the Hamas delegation in Cairo told Ward that he believed some agreement would be reached "within a few hours."
According to the source, Israel wants Hamas to stop rocket fire for an initial 24 hours, and then the Jewish state would theoretically meet some of the militant group's demands.
Ward notes, however, that previous remarks from diplomats suggesting a deal was near have proven premature, as Israel remains reluctant to accept Hamas' key demand that a total blockade on the Gaza Strip be lifted. Israel fears that lifting the blockade would allow more weapons to flow into the tiny Palestinian territory.
Israel has not formally said a deal has been reached, and even Hamas officials issued conflicting comments earlier Tuesday about an agreement. A senior Hamas official told The Associated Press that his group was only close to a cease-fire after the Reuters news agency reported a deal had been reached.
Hamas' Moussa Abu Marzouk told the AP from Cairo that "we haven't struck the deal yet, but we are progressing and it will most likely be tonight," after the other official, Ayman Taha, told Reuters that "an agreement for calm has been reached."
Another Hamas official, Izzat Risheq, said later that a deal might not be reached.
Throughout the day, relentless airstrikes and rocket attacks between the two sides continued. The Israeli death toll rose to five with the deaths Tuesday of an Israeli soldier and a civilian contractor. More than 130 Palestinians have been killed since Israel began air strikes last Wednesday.
Israeli officials said only that "intensive efforts" were under way to end the fighting.
In what appeared to be a last-minute burst of heavy fire, Israeli tanks and gunboats shelled targets late Tuesday, and an airstrike killed two brothers riding on a motorcycle. The men weren't identified.
The fighting came shortly before Clinton arrived. President Obama dispatched her to the Mideast from Cambodia, where she had accompanied him on a visit.
Morsi, perhaps the most important interlocutor between Hamas, which rules the Palestinian territory, and the Israelis, said the negotiations between the two sides would yield "positive results" during the coming hours.
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.
In Brussels, a senior official of the European Union's foreign service said a cease-fire would include an end of Israeli airstrikes and targeted killings in Gaza, the opening of Gaza crossing points and an end to rocket attacks on Israel. The official spoke on condition of anonymity because he was not authorized to speak to the media.
U.N. Secretary-General Ban Ki-moon spoke to both Israeli President Shimon Peres and Egyptian Prime Minister Hesham Mohamed Qandil Tuesday night, insisting a cease fire be reached immediately.
"The world is concerned, gravely concerned at the rising loss of human lives," he said. "Further escalation would be dangerous and tragic for Palestinians and Israelis, and would put the entire region at risk."
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. The men 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 it served as a Hamas communications post.
Of the 133 Palestinians killed, Gaza health officials said54 were civilians. Some 840 people have been wounded, including 225 children, in the Israeli air onslaught that has so far included nearly 1,500 strikes.
Five Israelis, including an 18-year-old soldier and a civilian contractor who worked for the military struck by rocket fire on Tuesday, have also been killed and dozens wounded since the fighting began last week, the numbers possibly kept down by a rocket-defense system that Israel developed with U.S. funding. More than 1,000 rockets have been fired at Israel this week, the military said.
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. In other violence, a 60-year-old Israeli woman was seriously wounded in a firebombing attack as she drove in the West Bank, police said.
With the death toll rising, the international community stepped up efforts to bring a halt to the fighting that began last Wednesday with an Israel's assassination of the Hamas military chief.
"If a long-term solution can be put in place through diplomatic means, then Israel would be a willing partner to such a solution. But if stronger military action proves necessary to stop the constant barrage of rockets, Israel wouldn't hesitate to do what is necessary to defend our people," Israeli Prime Minister Benjamin Netanyahu said during a joint press conference in Jerusalem with visiting U.N. chief Ban Ki-moon.