Thick smoke billowed in Gaza City after Israeli strikes on Sunday, as Israel's leaders vowed to press on with a planned offensive on the city.

Israeli planes and tanks pounded its eastern and northern outskirts overnight, destroying buildings and homes, residents said.

Palestinians were seen mourning loved ones, who they said were killed in the attacks, including children.

This woman said her nine-year-old nephew, Hamada Abedrabo, was leaving home to buy food when he was hit.

The boy's father said the family were there having been displaced from Jabalia in the north.

"The houses are gone, everything is gone and my son is gone," he said.

Adding that he hoped this would be the "last sad thing, and for this ordeal to end."

Israel approved a plan this month to seize control of Gaza City, describing it as Hamas' last bastion.

It is not expected to begin for a few weeks, leaving room for mediators Egypt and Qatar to try and resume ceasefire talks.

Israel's defense minister Israel Katz on Sunday vowed to push on with the offensive, which has raised alarm abroad and triggered protests at home.

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On Friday, Katz said Gaza City will be razed, unless Hamas agrees to end the war on Israel's terms and release all remaining hostages.

In a statement on Sunday, Hamas said Israel's plan to take over Gaza City showed it wasn't serious about a ceasefire, saying a ceasefire deal was QUOTE "the only way to return the hostages".

Around half of the enclave's two million people are living in Gaza City.

A few thousand have left, while some say they will not leave, no matter what.

Osama Kohail questioned where he could go, as he described a previous attempt to reach what was said to be a humanitarian zone in the southern city of Khan Younis.

"We were told to go to safe zones, to go to al-Mawasi," he said.

"We went to al-Mawasi. We saw humiliation and difficulties in al-Mawasi."

Israel pounds Gaza City suburbs, vows to press on with offensive