Israel and Hamas have put into effect an unconditional 72-hour humanitarian ceasefire in Gaza.
However, just hours after the truce began on Friday morning, Palestinian officials said four people had been killed by Israeli fire, apparently in response to a rocket attack.
Israel accused Hamas of a "flagrant violation" of the ceasefire, but correspondents say Gaza in general appears relatively quiet, the BBC reports.
Israel says it aims to stop rocket attacks by Palestinian militants in Gaza and remove the threat of being attacked from the tunnels.
Hamas wants a blockade of Gaza, maintained by both Israel and Egypt, to be lifted.
Earlier, in a joint statement, US Secretary of State John Kerry and UN Secretary-General Ban Ki-moon said the ceasefire was critical to giving innocent civilians a much-needed reprieve from violence and would begin at 8am (local time) on Friday.
Forces on the ground would remain in place during the truce, the statement said, implying that Israeli troops would not withdraw.
"We urge all parties to act with restraint until this humanitarian ceasefire begins, and to fully abide by their commitments during the ceasefire," they said.
Israel launched its military offensive in Gaza on 8 July with the aim of stamping out persistent militant rocket fire on southern Israel. On 17 July it expanded the operation by sending in ground troops to destroy tunnels used by militants.
Gaza officials say at least 1410 Palestinians, most of them civilians, have been killed in the battered territory and nearly 7000 wounded. Fifty-six Israeli soldiers have been killed in Gaza clashes and more than 400 wounded. Three civilians have been killed by Palestinian shelling in Israel.
US condemns Israel's school attack
In its strongest criticism yet of Israel's military operations in Gaza, the United States has said the shelling this week of a UN shelter is "totally indefensible".
At least 15 people were killed on Wednesday, when shellfire hit a UN-run school designated as a civilian shelter in the Jabaliya district of Gaza City.
"The shelling of a UN facility that is housing innocent civilians who are fleeing violence is totally unacceptable and totally indefensible," White House spokesman Josh Earnest said.
Israel's prime minister Benjamin Netanyahu has said that with or without a ceasefire, Israel is determined to destroy tunnels built by Palestinian militants to infiltrate into Israel from Gaza.
The Israeli military estimated on Wednesday that accomplishing that task, already into its fourth week, would take several more days.
The Pentagon called on Israel to do more to protect civilian life during its military operations in Gaza.
"The civilian casualties in Gaza have been too high. And it's become clear that the Israelis need to do more to live up to their very high standards - their very high and very public standards - for protecting civilian life," spokesman Colonel Steve Warren said.
UN Secretary-General Ban Ki-moon had earlier strongly condemned the deaths of those sheltering at the school and said its initial assessment was that Israeli artillery shells hit the facility, Reuters reports.