Israel declared a unilateral ceasefire at 2 a.m. local time (0000 GMT) on Sunday after three weeks of fighting, saying it had achieved all its objectives. At the same time, Israel said its troops would remain in the enclave.
It is still not clear how many troops will remain in Gaza and until when. "We can only confirm we have started a gradual withdrawal from the Gaza Strip," the spokeswoman said.
Hamas, which controls Gaza, also declared an immediate ceasefire several hours after Israel's announcement, adding that the militants had given Israel a week to pull its troops out of the enclave of 1.5 million.
Ismail Haniya, the de facto prime minister of Gaza, said Israel had failed to reach its goals. "We have won an historic victory, which will lead to the creation of a Palestinian state," he said.
He also suggested that the fighting had opened the way to reconciliation between the pro-presidential Fatah movement, which controls the West Bank, and Hamas.
Haniya thanked the international community for its support during Israel's attack, and called for the establishment of a commission to investigate Israel's actions in Gaza.
Israel launched its attack on Gaza on December 27, targeting Hamas infrastructure in a bid to put an end to rocket attacks by Palestinian militants on Israeli border towns. The military operation left over 1,300 Palestinians dead, the majority of them civilians. Thirteen Israelis, 10 of them military personnel, lost their lives in the fighting.