GAZA CITY - The Islamist Hamas movement fired more rockets at Israel Sunday, despite claims it had accepted a UN request for a 24-hour extension of a humanitarian truce in war-torn Gaza.

Hamas'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 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 AFP, adding another five were intercepted.

"They are violating their own ceasefire," Prime Minister Benjamin Netanyahu told the CNN news network. 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 1,031, 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 cease-fire 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 coexist 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 coexist 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 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.

In Rome, Pope Francis pleaded for an end to the bloodshed which has killed more than 1,000 victims, around a quarter of them children.

"Stop, please stop! I beg you with all my heart," he said in the weekly Angelus prayer.

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.

Shortly afterwards, the skies of Gaza were filled with the familiar sound of explosions, as plumes of black smoke rose on the horizon, an AFP correspondent in Gaza City said.

Ambulance sirens wailed as medics sprang into action, cars racing down streets which quickly emptied of people who had ventured out to make the most of the lull.

For Israelis, the quiet ended late on Saturday with air raid warnings sounding along the coastal plain as rockets hit the south and centre, killing a soldier and raising to 43 the number of troops killed since the July 17 start of a ground operation to destroy tunnels leading from Gaza to Israel.

Two Israeli civilians and a Thai agricultural worker have also been killed by rocket fire.

By Sunday morning, there appeared to be little appetite in Israel to prolong the one-sided truce, with 86.5 percent of Israelis opposing any ceasefire in the current climate, army radio said, quoting pollsters Mina Tzemah.