The ceasefire began early on Friday, bringing to an end 11 days of bombardment in which more than 240 people have died, most of them in Gaza.
Palestinians poured on to the streets of Gaza soon after the truce began, while a Hamas official warned that its hands “are on the trigger”.
Both Israel and Hamas have claimed victory in the conflict.
US President Joe Biden said the ceasefire brought “genuine opportunity” for progress.
On Thursday more than 100 Israeli air strikes targeted Hamas infrastructure in the north of Gaza. Hamas retaliated with rocket fire.
Fighting began in Gaza on 10 May after weeks of rising Israeli-Palestinian tension in occupied East Jerusalem that culminated in clashes at a holy site revered by both Muslims and Jews. Hamas began firing rockets after warning Israel to withdraw from the site, triggering retaliatory air strikes.
At least 232 people, including more than 100 women and children, have been killed in Gaza, according to its Hamas-controlled health ministry. Israel has said at least 150 militants are among those killed in Gaza. Hamas does not give casualty figures for fighters.
In Israel 12 people, including two children, have been killed, its medical service says. Israel says some 4,000 rockets have been fired towards its territory by militants in Gaza.
