A three-day truce has come into effect between Israel and the Palestinians in Gaza, after a day of intense diplomacy.
It is hoped the latest truce, which came into effect at 21:00 GMT, will help negotiators agree a longer peace.
Egypt brokered a similar truce last week, but fighting resumed after the three-day window ended.
About 2,000 people have died in the conflict, which began on 8 July when Israel launched an operation to deter militant attacks from Gaza.
Those killed include more than 1,900 Palestinians, mostly civilians, according to the UN. Sixty-seven people have died on the Israeli side, including three civilians.
Israeli media were reporting warning sirens for rocket attacks right up to the new ceasefire deadline at midnight local time. Israeli air strikes also continued through Sunday evening.
However, an hour into the ceasefire there were no reports of attacks from either side.
Israeli air strikes and Palestinian rocket fire continued on Sunday
Part of the Palestinians’ demands are that the blockade of Gaza’s borders is ended
After tense talks that both sides had threatened to abandon, the surprise announcement of the truce came late on Sunday.
“Israel has accepted Egypt’s proposal for a 72-hour ceasefire,” a senior Israeli official told the BBC.
The official added that Israel would send negotiators to Cairo on Monday if the truce holds.
Izzat al-Reshiq, a Hamas negotiator in Cairo, told Reuters news agency: “In light of Israel’s acceptance of the truce and their return without pre-conditions, we will inform the Egyptian brothers of our positive response.”
In a statement, Egypt’s foreign ministry urged both sides to resume indirect negotiations and “work towards a comprehensive and lasting ceasefire agreement”.
Israeli soldiers continued to search for tunnels used by militants on Sunday
Protesters on both sides were out on the streets of Washington
Correspondents say Israel is likely to continue to push for Gaza to be demilitarised, and Hamas will continue to demand the blockade of Gaza to be lifted.
The issues have scuppered previous talks, conducted through intermediaries.
However, an unidentified Hamas negotiator said their demands were likely to be “more modest” this time.
Since the last 72-hour truce ended on Friday, there has been regular exchange of fire.
Israeli air strikes have killed at least 20 Palestinians. Two Israelis were injured by mortars.
The BBC’s Wyre Davies in Jerusalem says the ceasefire should allow more humanitarian aid into Gaza, where thousands have been left homeless.
On the Israeli side, where dozens of communities have been evacuated, residents will also be able to return home.