Israeli Defence Minister Israel Katz said early Tuesday that Gaza City, the territory's main urban hub, was "on fire".

"We will not relent and we will not back down until the mission is accomplished," Katz said.

Witnesses told AFP of heavy, relentless bombing on Gaza City, much of which is already in rubble after nearly two years of Israeli bombardment since the October 7, 2023 attacks by Hamas.

"We can hear their screams," said 25-year-old resident Ahmed Ghazal.

Rubio on Monday offered robust backing for the offensive as he met Israeli Prime Minister Benjamin Netanyahu, who has asked the Israeli military to seize Gaza City.

Pointing to the fresh operations, Rubio told reporters as he left Israel: "We think we have a very short window of time in which a deal can happen. We don't have months anymore, and we probably have days and maybe a few weeks to go."

Rubio said a diplomatic solution in which Hamas demilitarises remained the US preference, although he added: "Sometimes when you're dealing with a group of savages like Hamas, that's not possible, but we hope it can happen."

Rubio, who met Monday in Jerusalem with families of hostages in Gaza, acknowledged that Hamas had leverage by holding them.

"If there were no hostages and no civilians in the way, this war would have ended a year and a half ago," he said at Tel Aviv's Ben Gurion airport.

A group representing hostages families said they were "terrified" for their loved ones after Netanyahu ordered the strikes.

"He is doing everything to ensure there is no deal and not to bring them back," they said in a statement.

- US still hopes for Qatar role -

Rubio was flying to Qatar, which he said he hoped would keep up its mediation, despite Israel carrying out air strikes a week ago in the Gulf country against Hamas leaders gathered to consider a US truce proposal.

"We want them to know that if there's any country in the world that could help end this through a negotiation, it's Qatar," Rubio said.

President Donald Trump said that Netanyahu would not be hitting Qatar again, although both Rubio and Netanyahu declined to make similar assurances.

European powers, but not the United States, have unsuccessfully urged Israel to halt the new Gaza campaign, warning of worsening the humanitarian crisis in the territory, where the United Nations determined last month a million people were facing famine -- a finding rejected by Israel.

Mahmud Bassal, a spokesman for the Gaza civil defence agency, told AFP that as of early Tuesday heavy bombing was ongoing in Gaza City "and the number of deaths and injuries continues to rise".

Bassal said the Israeli military also targeted the southern city of Khan Yunis, after the civil defence agency reported Israeli strikes killed 49 people on Monday.

Media restrictions in Gaza and difficulties in accessing many areas mean AFP is unable to independently verify the details provided by the civil defence agency or the Israeli military.

- Ahead of French statehood push -

Rubio's visit and the Israeli strikes come a week before France will lead a UN summit in which a number of Western countries, angered by what they see as Israeli intransigence, plan to recognise a Palestinian state.

Rubio called statehood recognition "largely symbolic", while Netanyahu -- whose government is fervently opposed to such a move -- said his country may take unspecified "unilateral steps" in response.

Far-right members of Netanyahu's cabinet have called for annexation of the occupied West Bank to preclude a state, triggering protests by the United Arab Emirates, which normalised ties with Israel five years ago.

Netanyahu said Rubio's visit was a "clear message" the United States stood with Israel, and called Trump "the greatest friend that Israel has ever had".

The October 7 attack by Hamas resulted in the deaths of 1,219 people, most of them civilians, according to an AFP tally of official figures.

Israel's retaliatory campaign in Gaza has killed more than 64,900 people, also mostly civilians, according to figures from the territory's health ministry that the United Nations considers reliable.

Of the 251 people taken hostage by Palestinian militants in October 2023, 47 remain in Gaza, including 25 the Israeli military says are dead.