A 24-hour ceasefire announced by Hamas in Gaza appears to be stalling, with both Palestinian militants and Israel continuing their offensives.
Hamas fired more rockets into Israel, accusing it of failing to abide by the ceasefire.
Israel rejected the truce, PM Benjamin Netanyahu saying: "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.
The latest developments further undermined hopes that Saturday's humanitarian truce observed by both sides could be extended.
Israel later accepted a UN-requested 24-hour ceasefire until the end of Sunday, although it said ground forces would continue to destroy tunnels used by Hamas.
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 has controlled Gaza since seizing power there in 2007.
Shortly after Israeli raids resumed, Hamas said it had decided to agree to a humanitarian truce, starting at 14:00 local time (11:00 GMT).
The pause was "as a preparation for the end of (the Islamic holy month of) Ramadan and in response to the UN mediation and also regarding our people's living circumstances".
But in an interview with CNN, Netanyahu said: "Hamas doesn't even accept its own ceasefire. It's continuing to fire at us as we speak".
Israel launched its military offensive on 8 July 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.
Before 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.
At least 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.