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The agreement, which began at midnight (21:00 GMT Sunday), came after days of intense mediation by Egypt.
If the truce continues to hold, Israel will send negotiators to Cairo on Monday for talks on a longer-term deal.
About 2,000 people have died in the conflict, which began on 8 July when Israel launched an operation intended 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.
Minutes before the ceasefire began, militants claimed to have fired several rockets at Israel, including one at Tel Aviv, but there were no reports of damage.
Israeli air strikes also continued throughout Sunday evening.
The Ynet website said the Israel Defense Forces had killed a militant in a tunnel in north Gaza before the ceasefire started.