A seven-hour "humanitarian window" announced by Israel has come into effect in parts of Gaza. A senior Israeli military official said the ceasefire would not apply to the town of Rafah and that Israeli troops would respond if they were attacked. Palestinian officials have accused Israel of breaking the truce with a strike on a house in Gaza City.
The Israeli announcement came after a attack near a UN-run school in Gaza on Sunday sparked international outrage. Palestinian officials said at least 10 people died in the attack on Sunday.
Earlier, the Israel Defense Forces (IDF) confirmed that they had begun withdrawing some troops from Gaza, saying they were "extremely close" to completing their mission to destroy a network of tunnels. Health officials in Gaza say 1,800 Palestinians, most of them civilians, have been killed and more than 9,000 injured since the conflict began nearly four weeks ago. Sixty-six Israelis have died, all but two of them soldiers. A Thai national working in Israel was also killed.
Previous ceasefires and truces have all come and gone in Gaza. Most have crumbled within a matter of hours. And while Israel has announced a "humanitarian window", nobody here has any faith in it.
Israel says that it will continue its military operations close to the southern town of Rafah. Just minutes after the ceasefire got under way, Palestinians say Israel carried out in airstrike inside Gaza city - an area that was supposed to be covered by the truce.
We heard the explosion at our Gaza bureau. A BBC team saw a house that had been destroyed - locals say that at least one person died and others were injured in the attack. There's yet to be any word from the Israeli military. But it's for this reason that Palestinians say that no place in Gaza is safe - ceasefire or not.
The news that the Israeli army has redeployed some of its troops along the Gaza border and announced a partial humanitarian ceasefire for a few hours, has prompted some speculation that it may be trying to wind down the military operation unilaterally, without an agreed ceasefire with Hamas.
But it is by no means clear that an end to the fighting is in sight. The offensive around Rafah, near the Egyptian border, continues, possibly to try and make it harder for Hamas to re-arm in future. And the army may be searching for more cross border tunnels that it has not yet identified.
There is intense international pressure on Israel to negotiate a long-term ceasefire. For now, Israel appears to be ignoring those calls, but it hasn't ruled out a possible diplomatic solution.
Violation of truce?
Hamas responded to the truce with suspicion, accusing the IDF of trying to "divert the attention from Israeli massacres".Palestinian health officials claim Israel carried out an air strike on a refugee camp inside Gaza City just minutes after the ceasefire began. BBC correspondents there said they heard the explosion and saw a house that had been destroyed in the attack. Reports suggest the strike killed a young girl and injured at least 15 others, many of them women and children.
Israel's temporary ceasefire - aimed at allowing Palestinians to return to their homes - would not include Rafah because there was an "Israeli military presence" there and "clashes were still ongoing", the IDF said.
The truce began at 10:00 local time (07:00 GMT) and is due to last until 17:00 (14:00 GMT). The Israeli army warned that it would "respond to any attempt to exploit this window" by Islamist militants.
Israeli air strikes on Gaza and Palestinian militant rocket fire launched at Israel continued on Monday morning ahead of the planned ceasefire.
The Islamic Jihad group said its commander in northern Gaza, Daniel Mansour, died when Israeli forces struck his home just before dawn.
More than a quarter of the 1.8 million residents in the Palestinian territory have been displaced in the most recent hostilities.Many of those who have fled their homes have taken refuge in UN shelters across Gaza, including the UN-run school in Rafah which was hit on Sunday. The IDF said it had targeted three Islamist militants near the school. UN chief Ban Ki-moon described the Israeli strike as "a criminal act" and the US said it was appalled by the "disgraceful shelling".
Israeli Prime Minister Benjamin Netanyahu on Monday said Israel was "sorry for any attack that unintentionally hits civilians", but accused Hamas of turning UN facilities into "terrorist hotspots".
The IDF says 2,560 rockets and mortars fired from Gaza have landed in Israel since 8 July, and that its Iron Dome defence system has intercepted another 556 rockets.