Hamas has fired more rockets at Israel, despite claims it had accepted a UN request for an extension of a humanitarian truce in war-torn Gaza.

The Islamist movement’s belated acceptance of diplomatic calls for a temporary ceasefire was announced several hours after Israel resumed its devastating military assault on the Palestinian enclave after a pause of more than 24 hours.

Although Hamas said its militants would halt their fire from 1100 GMT (2100 AEST) in response to a request from the United Nations, there was no response from Israel.

And Palestinian rocket fire continued, with 22 striking the Jewish state after the reported truce went into effect, an army spokeswoman told news agency AFP, adding that another five were intercepted.

“They are violating their own ceasefire,” Prime Minister Benjamin Netanyahu told CNN.

In a separate interview with CBS, he said Israel would not allow “a ruthless terror organisation … to decide when it’s convenient for them to stop for a moment, rearm, and continue firing on our citizens and our people”.

The abortive Hamas announcement came shortly after Israel said it would no longer abide by a unilateral ceasefire while coming under “incessant” fire from Gaza.

Shortly afterwards, Israel resumed its punishing air strikes and tank fire, killing 11 people across the territory, including an elderly Christian woman, medics said.

Another three people also succumbed to their wounds, raising the Palestinian toll on day 20 of Israel’s devastating military campaign to 1031, Gaza’s emergency services said.

The renewed violence came after a rare 12-hour cessation in hostilities on Saturday, which was respected by both sides, with world powers urging Israel and Hamas to extend the temporary truce by another day.

“The Secretary-General urges, in the strongest terms, both the Israelis and Palestinians to extend, for an additional 24 hours, the humanitarian ceasefire that was in effect and mostly observed until early this morning,” a statement from UN chief Ban Ki-moon’s spokesman said.

Exiled Hamas leader Khaled Meshaal said his group could not co-exist with Israel as long as it occupied Palestinian land.

“We are not actually fighting the Jews because they are Jews,” he said in remarks broadcast Sunday. “We fight the occupiers.”

“I’m ready to co-exist with the Jews, with the Christians and the Arabs and non-Arabs,” he said.

“However, I do not coexist with the occupiers.”

In Washington, a US official said Secretary of State John Kerry was pressing efforts for further pauses in the fighting, after he returned early on Sunday from a week-long mission to the Middle East, which failed to produce a long-term ceasefire.

Israeli media said Netanyahu’s security cabinet was meeting on Sunday evening to discuss the next steps.

Saturday’s relative calm was a distant memory by Sunday.

“I was praying at church when my father called me and told me to go home quickly,” said Antonio Ayyad, a Christian whose elderly mother was killed when a missile hit their home in western Gaza City.

“They are targeting Christians in Gaza,” he said.

“I’m not Hamas, I’m not Fatah – I don’t belong to any Palestinian faction. Where is the world? Where is the pope?” he asked.

Following Saturday’s humanitarian lull, Israel agreed to extend the truce by 24 hours but Hamas fired rockets over the border, one of which killed a soldier.

Then, after 12 hours of holding its fire, Israel said it was resuming operations following “incessant” Hamas rocket fire.