A seven-hour "humanitarian window" announced by Israel has come into effect in parts of Gaza.
A senior Israeli military official said the truce would not apply to the town of Rafah and that Israeli troops would respond if they were attacked.
Earlier, United Nations chief Ban Ki-moon described an Israeli strike near a UN-run school in Gaza as "a moral outrage and a criminal act".
Palestinian officials said at least 10 people died in the attack on Sunday. The Israel Defense Forces (IDF) confirmed on Sunday that they had begun withdrawing some troops from Gaza, saying it was "extremely close" to completing its 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.
In the outrage that followed Sunday's attack on the UN school, Israel announced it would hold a "humanitarian window" in its Gaza offensive to allow hundreds of thousands of displaced Palestinians to return to their homes.
The ceasefire would not include Rafah because there was an "Israeli military presence" there and "clashes were still ongoing", an IDF statement said. It said the truce would last from 10:00 local time (07:00 GMT) until 17:00 (14:00 GMT).
The Israeli army warned that it would "respond to any attempt to exploit this window" by Islamist militants in Gaza.
Hamas responded to the truce with suspicion and its spokesman, Sami Abu Zuhri, accused the IDF of attempting to "divert the attention from Israeli massacres".
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. 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. Mr Ban described the attack as "yet another gross violation of international humanitarian law", adding that Israel had regularly been informed of the precise location of the school.
State Department spokeswoman Jen Psaki said the US was appalled by the "disgraceful shelling".
Israel said it was investigating the incident. Prime Minister Benjamin Netanyahu said Israel was "sorry for any attack that unintentionally hits civilians", but accused Hamas of turning UN facilities into "terrorist hotspots".
"Hamas has an interest in Gaza residents suffering, thinking that the world will blame Israel for their suffering," Mr Netanyahu said in a statement on Monday.
The IDF says 2,560 rockets and mortars fired from Gaza have landed in Israel since 8 July, with its Iron Dome defence system having intercepted another 556 rockets.