Egypt has proposed a ceasefire to end a week of cross-border fire between the Gaza Strip and Israel.
The initiative urges a ceasefire starting imminently followed by a series of meetings in Cairo with high-level delegations from both sides.
However an official from Hamas, which controls Gaza, said a full deal would have to come first, before a ceasefire.
Israeli officials said PM Benjamin Netanyahu's security cabinet would discuss the proposal early on Tuesday.
Palestinian officials say at least 185 people in Gaza have been killed by Israeli air strikes since the offensive began last Tuesday. The UN estimates that over three-quarters of these were civilians.
Israel says nearly 1,000 rockets have been fired from Gaza in that time. No Israelis have been killed although several have been injured.
At least three rockets landed in and around the southern Israeli city of Eilat, Israeli officials said. Reports suggest they may have been fired from the Sinai peninsula in Egypt.
A senior Israeli official told the BBC that Hamas was "much weaker" after air strikes destroyed many of its rockets and manufacturing facilities.
Status quo 'unsustainable'
The ceasefire calls come ahead of an urgent meeting of Arab League foreign ministers in Cairo.
Hamas, the faction that controls Gaza, confirmed that truce efforts were under way.
But a Hamas official told the AFP news agency that a political agreement must be reached before a ceasefire could take effect.
"A ceasefire without reaching an agreement is rejected. In times of war, you don't cease fire and then negotiate," said spokesperson Fawzi Barhum.
A spokesman for Hamas' armed wing said that they had received no official notification of the ceasefire proposal, and said that the reported terms were a "surrender".
US President Barack Obama welcomed the Egyptian proposal, and said the deaths of Palestinian civilians was a "tragedy".
"We're going to continue to do everything we can to facilitate a return to the 2012 ceasefire," he said, adding that the "that the status quo is unsustainable".
Thousands of people fled their homes in northern Gaza on Monday after an Israeli warning of intensified air strikes and Israel has also massed thousands of troops on the border, amid speculation of a possible ground invasion.
Ismail Haniyeh, a Hamas leader in Gaza, said in a speech broadcast on al-Jazeera that Hamas was not only seeking an end to the fighting but also an easing of the Israeli blockade that has crippled life in Gaza.
"The problem is the reality of Gaza, the siege, the starving, the bombing. The siege must stop and people in Gaza need to live in dignity," he said.
Israel imposed a blockade on Gaza when Hamas - which is designated a terrorist group by Israel, the US and other countries - took over in 2007. Hamas won the Palestinian legislative elections in 2006.
Israel is demanding an end to rocket attacks on its towns and cities from Gaza.
The BBC's Orla Guerin in Cairo says Egypt has been accused of failing to play its usual role of mediator between Israel and Hamas.
After a week of bloodshed, it has now at least produced a blueprint for a deal, she adds.
In 2012 Egypt's then-President Mohammed Morsi brokered a ceasefire between Hamas and Israel, using the influence his Muslim Brotherhood held with the Palestinian group.
The current outbreak of violence followed the killing of three Israeli teenagers in June and the suspected revenge killing of a Palestinian teenager in Jerusalem.
Israeli officials said on Monday that three arrested Israeli Jews had confessed to the murder of the Palestinian, Mohammed Abu Khdair.
The three, whose names have not been released, have been remanded in custody.
The UN estimates that 77% of those killed in Gaza have been civilians.
However Israel disputes the figures, saying they are based on Hamas sources and are not objective.
A military spokesman told the BBC that Israel had aborted some attacks for fear of killing civilians.
Israel says it is targeting Hamas militants and "terror sites", including the homes of senior operatives.
In a statement, the Israeli Defense Forces (IDF) said: "We do not wish to harm civilians in Gaza, but these civilians must know that remaining in close proximity to Hamas terrorists and infrastructures is extremely unsafe."