Israeli Prime Minister Benjamin Netanyahu has said the seven-week conflict in Gaza ended in "victory".
The Palestinian Islamist Hamas movement was "hit hard and got none of its demands," Mr Netanyahu said.
Hamas has also claimed the truce represents a victory for Gaza and held a large rally to celebrate it.
On Tuesday a ceasefire came into effect after 50 days of fierce fighting in which more than 2,200 people died, most of them Palestinians.
In a televised news conference, Mr Netanyahu said Hamas had been "hit hard" and threatened an even tougher response should there be so much as a "sprinkle" of rocket fire from Gaza.
He added that Israel "didn't agree to accept any of Hamas' demands".
On Wednesday, the UN's World Food Programme said one of its convoys had entered Gaza from Egypt for the first time since 2007, carrying enough food to feed around 150,000 people for five days.
Fishing boats also ventured out to sea as restrictions were eased.
Thousands of Palestinians began to return to their homes as the truce held for the whole of Wednesday.
Engineers meanwhile struggled to repair infrastructure damaged by Israeli air strikes and shellfire.
In Israel, sirens warning of incoming rocket fire were silent and the military said there had been no violations of the ceasefire since it took effect.
UN Secretary General Ban Ki-moon welcomed the end of hostilities, but warned that a brighter future for civilians who have been affected depends on a sustainable truce.
"After 50 days of profound human suffering and devastating physical destruction, any violations of the ceasefire would be utterly irresponsible," he said.
The ceasefire deal calls for the relaxing of Israeli and Egyptian border controls to allow humanitarian supplies and construction materials into Gaza, and the widening of the territory's fishing zone.
Both sides have agreed to address more contentious issues - including Palestinian demands for a seaport in Gaza and the release of Hamas prisoners in the West Bank, and Israel's demand for Gaza's militants to be disarmed - at indirect talks that should begin in Cairo within a month.
Israeli media reported that Mr Netanyahu had chosen not to put Egypt's ceasefire proposal to a vote in his security cabinet because of opposition from ministers who wanted to continue the offensive on Gaza.
Israel launched Operation Protective Edge on 8 July with the stated aim of ending rocket fire.
At least 2,140 people, most of them civilians, have been killed in Gaza, according to the Palestinian health ministry. Another 11,000 people have been injured.
The Israeli authorities say 64 Israeli soldiers have been killed, along with six Israeli civilians and a Thai national.
The UN says more than 17,000 buildings in Gaza have been destroyed or severely damaged, and that there are at least 475,000 internally displaced people (IDPs), more than a quarter of the territory's population.
Correction 18 September: An earlier reference to the World Food Programme's aid delivery has been amended to make clear that the convoy entered Gaza from Egypt for the first time since 2007. The WFP was already making deliveries into Gaza via Israel.