Palestinian militant group Hamas has announced a 24-hour ceasefire after Israel ended its own truce amid continuing rocket fire from Gaza.
All Palestinian militant factions would stop firing from 11:00 GMT, Hamas said.
But Israeli PM Benjamin Netanyahu said Hamas had already violated its own ceasefire and "Israel will do what it must do to defend its people".
More than 1,060 Palestinians, mostly civilians, and 43 Israeli soldiers and two Israeli civilians have been killed.
A Thai national in Israel has also died.
In a more explicit response to the Hamas ceasefire, an Israeli official told the BBC Israel did not accept it.
Israel launched its military offensive with the declared objective of stopping Hamas firing rockets from Gaza into Israel.
On 18 July, it extended operations with a ground offensive, saying it was necessary to destroy tunnels dug by militants to infiltrate Israel.
'Incessant rocket fire'
On Saturday, Israel accepted a UN request for a 24-hour ceasefire until the end of Sunday, although it said ground forces would continue to destroy tunnels used by Hamas during the pause.
The Israeli ceasefire followed a 12-hour truce, observed by both sides on Saturday, which enabled Gaza residents to gather supplies and retrieve bodies buried under the rubble.
However, the Israeli military announced on Sunday morning it had decided to resume its air, ground and naval raids on Gaza in response to "incessant rocket fire" from Hamas, which controls Gaza.
Hamas had initially rejected the Israeli offer, saying it would only halt rocket attacks once Israeli troops left Gaza and the displaced were allowed to return home.
But shortly after Israeli raids resumed, Hamas said it had decided to agree to a humanitarian truce.
"As a preparation for the end of Ramadan and in response to the UN mediation and also regarding our people's living circumstances, we have agreed with all Palestinian factions to give a 24-hour humanitarian ceasefire starting from 14:00 on Sunday," Hamas spokesman Sami Abu Zuhri said in a statement.
Before Mr Netanyahu's comments, an Israeli military spokesman, Col Peter Lerner, suggested the Hamas announcement might be an "opportunity perhaps" while cautioning: "This is a bit premature and we are watching the situation carefully."
Correspondents in Gaza said loud explosions could be heard in several districts as Israeli forces resumed their air strikes. Palestinian eyewitnesses reported heavy shelling to the east of Gaza City.
Eight Palestinians have died in Sunday's attacks, according to Gazan health officials.
The Israel Defense Forces (IDF) said 28 rockets have been fired from Gaza into Israel on Sunday. Two more rockets were intercepted by the Iron Dome missiles defence system, the IDF said. It did not say if any of the firing was after the Hamas-announced ceasefire.
It added that a soldier was killed by mortar shell fired from Gaza early on Sunday morning.