US President Joe Biden has said a two-state solution is the only answer to resolving the conflict between Israel and the Palestinian people.
The US administration worked in the background, along with Egypt, to secure an end to the conflict which lasted 11 days.
Some 248 Palestinians - including 66 children - died, while 12 people in Israel died.
The ceasefire came into effect at 2am local time - 12am UK time - on Friday.
Mr Biden has said that the US will work with the internationally recognised Palestinian Authority, and not Hamas, in order to provide humanitarian aid to Gaza.
Since the ceasefire, the United Nations has sent 13 trucks with food, COVID vaccines and other medical supplies into Gaza, with $18.6m (£13.1m) in emergency humanitarian aid allocated to the region.
The US has said it will also help Israel replenish its supply of interceptor missiles.
Israeli Prime Minister Benjamin Netanyahu has threatened a "new level of force" if Hamas launches any attacks following the ceasefire.
"If Hamas thinks we will tolerate a drizzle of rockets, it is wrong," he warned.
Mr Biden, speaking at the White House, added: "Let's get something straight here: until the region says unequivocally they acknowledge the right of Israel to exist as an independent Jewish state, there will be no peace.
"I'm praying this ceasefire will hold. I take Bibi [Benjamin] Netanyahu - when he gives me his word - I take him at his word. He's never broken his word to me."
The ceasefire faced its first test on Friday afternoon, when tens of thousands of Palestinians attended Friday Prayers at Al-Aqsa mosque in Jerusalem - where tensions first began.
Some threw stones at Israeli police, who fired stun grenades and tear gas in return, in an echo of the scenes that triggered the 11-day conflict.
Twenty Palestinians were arrested at the gates, although it is unclear what started the clashes at the mosque - a holy site for both Muslims and Jews - who refer to it as the Temple Mount.
An Israeli Police foreign spokesman claimed "hundreds of people threw rocks and petrol bombs at police officers", saying Israeli forces "dispersed rioters".
There were similar clashes in the West Bank.
Sky News correspondent Mark Stone, who is in the region, said the elusive two-state solution was as far away as ever but that both sides were likely to gain politically.
Following the end of the conflict, people in Gaza who were sheltering in UN schools have since left the facilities.
From a peak of 66,000 people crammed into the shelters, less than 1,000 remain, according to a UN spokesperson.
Rescue workers have been recovering bodies, including one of a three-year-old girl, according to the Red Crescent emergency services.
The 11 days of fighting in Israel, Gaza and the West Bank was the worst seen in the region since 2014.
Hamas and other militant groups fired more than 4,000 rockets at Israeli cities, with Israel conducting hundreds of airstrikes.