Israel has warned it is prepared to resume military operations in Gaza if the Egyptian-brokered ceasefire is violated.
Israel launched an offensive which it says was aimed at ending rocket fire from Gaza, with the killing of a Hamas military leader last week.
The Israeli army has been withdrawing columns of vehicles from the border, while Hamas, which governs the territory, declared a public holiday on Thursday to mark what it is hailing as a victory.
The ceasefire came into force at 9pm on Wednesday. Israel has agreed to end all hostilities and targeted killings and must also begin talks about opening Gaza's border crossings, while all Palestinian factions have to stop firing rockets into Israel and staging border attacks.
Only if the ceasefire holds will talks begin on issues which have bedevilled the region for years and which will be long and difficult, the BBC reports.
They include whether the crossing point between Gaza and Egypt be open more often to more goods and more people without becoming a conduit for more weapons smuggled from Iran, and can Hamas rein in smaller groups of militants who might fire rockets purely to destory the ceasefire.
Palestinians also want the right to farm all the way up to the Israeli fence around Gaza, regaining the use of their own land from which they are currently barred by Israeli security measures.
The BBC reports a number of rockets were fired from Gaza in the first few hours of the truce, but Israel did not respond. However, Israeli schools close to the Gaza Strip were kept closed on Thursday as a precaution.
Meanwhile, Hamas has thanked Iran for its support during the conflict and confirmed that the country supplied long-range missiles that were fired into Israel.