"The ceasefire understanding will begin Monday 04:30 (0130 GMT)," a Palestinian official familiar with the agreement told Reuters news agency.
A second Palestinian official confirmed that a deal was reached, as well a TV station belonging to Hamas, the group that rules Gaza Strip.
There was no confirmation from the Israeli side.
Israel's military said that more than 600 rockets and other projectiles - over 150 of them intercepted by its Iron Dome anti-missile system - had been fired at southern Israeli cities and villages since Friday.
It said it attacked about 320 targets in Gaza.
The violence - the most serious border clashes since a spate of fighting in November - appeared to abate early on Monday. Rocket sirens in southern Israel, which had gone off continuously over the weekend, sending residents running for cover, were quite for a few hours straight before dawn.
Israel's military reported no new air strikes in Gaza.
Earlier, Israeli Prime Minister Benjamin Netanyahu had ordered "massive strikes" on the Gaza Strip after a two-day escalation.
Israeli warplanes and gunboats continued to target the Gaza Strip on Sunday as fighters in the besieged enclave fired a barrage of rockets into southern Israel.
A 34-year-old Hamas commander was killed in what the Israeli military described as a targeted strike. An army statement accused Hamad al-Khodori of "transferring large sums of money" from Iran to armed factions in Gaza.
He was the fifth Palestinian reported killed on Sunday. Other Palestinian victims included two pregnant women and three infants.
In the Israeli city of Ashkelon, a 58-year-old Israeli man was killed after being struck by shrapnel from a rocket attack. Two other Israelis, critically wounded in a separate rocket attacks on a factory on Sunday afternoon, later died.
Around two million Palestinians live in Gaza, the economy of which has suffered years of Israeli and Egyptian blockades as well as recent foreign aid cuts and sanctions by the Palestinian Authority, Hamas' West Bank-based rival.
Israel said its blockade is necessary to stop weapons reaching Hamas, with which it has fought three wars since the group seized control of Gaza in 2007, two years after Israel withdrew its settlers and troops from the area.