One rocket was launched by Hamas at Tel Aviv just before the ceasefire came into effect, the Israeli military said, and may have landed in the sea.
Previous efforts to secure a more lasting peace in the region have failed, and Israeli negotiators returned from Cairo on Friday.
However, with the new ceasefire in place talks will be resuming.
Hamas is calling for an end to Israel’s blockade of Gaza and the opening of a seaport in the area. Hamas spokesman Sami Abu Zuhri said the new negotiations would be “the last chance” for a deal.
Israeli Strategic Affairs Minister Yuval Steinitz said in a radio interview on Monday that disarming Gaza militants was crucial to sustain a long-term truce and he hoped this could be done by diplomacy rather than force.
“I certainly hope that there will be a diplomatic solution,” he said. “If there will not be a diplomatic solution, I am convinced that sooner or later we will have to opt for a military solution of taking temporary control of Gaza to demilitarise it again.”
Egypt’s Foreign Ministry, which is meeting separately with each side in Cairo, urged “both sides to exploit this truce to resume indirect negotiations immediately and work towards a comprehensive and lasting ceasefire agreement”.
Meanwhile, a third Palestinian is reported to have been killed in the West Bank during four days of clashes. Zakaria al-Aqra, 23, was wanted by Israel and was shot dead during a raid on his home, medical officials saud.
An Israeli military spokeswoman said she was aware of troop activity in the area but initially had no further details.