Cairo has proposed a ceasefire which would come into effect at 0600 GMT, with Israeli Prime Minister Benjamin Netanyahu convening ministers from his security cabinet to consider the offer, which has won support from Washington.
But the Islamist Hamas movement, whose militants have fired hundreds of rockets at Israel in the past week, ruled out any end to the fighting without a fully-fledged agreement as the death toll in Gaza from the seven-day conflict rose to 188.
Cairo's proposal came after Washington warned Israel against a ground offensive and as US Secretary of State John Kerry was due to arrive in Cairo to throw his weight behind diplomatic efforts to end the bloodshed, Egyptian state media reported.
US President Barack Obama welcomed the Egyptian initiative, describing the deaths of Palestinian civilians as a "tragedy" while expressing support for Israel's right to defend itself against rocket attacks.
"We are encouraged that Egypt has made a proposal to accomplish this goal that we hope can restore the calm that we are seeking," said Obama.
Israel launched Operation Protective Edge before dawn on July 8, hitting Gaza with an intensive aerial bombing campaign to stamp out cross-border rocket fire, with militants answering with hundreds of rockets, dozens of which have targeted central and even northern Israel.
The deadly conflict, which has claimed the most victims since Israel's blistering 22-day offensive in 2008-2009, has also seen rockets from Syria and Lebanon hitting the Israeli north, raising fears the conflict could spread.
Overnight, three rockets fired from Egypt's Sinai Peninsula hit Israel's Red Sea resort of Eilat, two of them inside the city, causing damage and one outside in an open area, the military said.
Only two projectiles had been fired from Gaza since midnight.
Details of the Egyptian proposal were laid out late on Monday.
"0600 GMT has been set for the beginning of the implementation of truce arrangements between the two sides," a statement said, with Cairo saying it would be willing to host talks between high-level Israeli and Palestinian delegations after the ceasefire went into effect.
Ministers from Israel's security cabinet began meeting to discuss the ceasefire agreement at 7:00 am (0400 GMT), army radio reported, saying up to three hardline ministers were likely to vote against it.
But Hamas rejected the idea, with spokesman Fawzi Barhum telling AFP there would be no truce without a fully-fledged deal to end hostilities.
"In times of war, you don't cease fire and then negotiate," he said.
Hamas had not received any official proposal, and even if Israel held its fire, it would have "no value" after the widespread damage it has wreaked in Gaza, he said.
And its militant wing, the Ezzedine al-Qassam Brigades, rejected the proposal as "surrender," pledging to "intensify" its attacks on Israel.
Hamas has said it will not hold its fire without Israel agreeing to a list of demands, including an end to its eight-year blockade on Gaza, along with the opening of the Rafah border crossing with Egypt.
It also wants Israel to free Palestinians it rearrested after releasing them in exchange for kidnapped Israeli soldier Gilad Shalit.
Palestinian president Mahmud Abbas welcomed the Egyptian initiative, as did the Arab League, which called on "all parties" to accept the truce.
Washington warned its Israeli ally against mounting a possible ground invasion of Gaza as the death toll from the air strikes spiralled, drawing criticism from the United Nations and rights watchdogs.
"Nobody wants to see a ground invasion because that would put more civilians at risk," White House spokesman Josh Earnest said.
It was the first time the White House has specifically warned in a public forum against an Israeli invasion of Gaza.
As the conflict entered its eighth day, the death toll hit 188, rising above the death toll from eight days of violence in the last major confrontation in November 2012.
Human rights groups say more than 75 percent of the dead have been non-combatants, and the UN agency for Palestinian refugees said more than a quarter were children.
Over the same period, 840 rockets have struck Israel, including Jerusalem, Tel Aviv and the northern city of Hadera. Israel's Iron Dome missile defence system has shot down 191, the army said.