Israel and Hamas have put into effect an unconditional 72-hour humanitarian ceasefire in Gaza.
However, hours after the truce began, Palestinians 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.
Israel says it is continuing to destroy tunnels built by Hamas into Israel.
Some 1,460 Palestinians, mostly civilians, have died in the conflict, health officials say. Sixty-three Israelis, mostly soldiers, have died.
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.
‘Much needed reprieve’
The BBC’s Jon Donnison in Gaza says that Israeli bombing and Palestinian rocket attacks continued until the start of the ceasefire but the skies are now quiet.
During the morning life appeared to be returning to some kind of normality in Gaza, with many Palestinians heading towards heavily shelled areas to see if their homes were still intact.
But the Gaza health ministry reported that four Palestinians were killed and dozens were injured in an Israeli attack near the southern town of Rafah after the ceasefire began.
Israeli military sources told the BBC the attack was in response to rocket fire on Kerem Shalom in Israel.
“Once again the terror organisations in Gaza flagrantly violating the ceasefire to which they committed themselves,” Israeli officials said without specifying any incident.
The BBC’s Martin Patience in Gaza says that compared to the violence of recent weeks much of Gaza is relatively quiet, and the breach does not mean the truce has broken down.
Announcing the ceasefire, the US and UN emphasised its humanitarian nature but said Israeli troops would be allowed to stay on the ground in Gaza.