Israel has heavily bombed Gaza City overnight with unconfirmed reports from the US news site Axios and the Jerusalem Post that the military has now launched its ground offensive to occupy the entire city.

Israeli strikes are also reported in central Gaza, in the direction in which thousands of people are fleeing. Palestinian officials say there are rising numbers of deaths and injuries.

The intensification came ahead of a long-threatened full-scale ground invasion of the city, which is home to hundreds of thousands of people.

It came hours after Secretary of State Marco Rubio assured Israeli Prime Minister Benjamin Netanyahu of unwavering US support during a trip to Jerusalem on Monday.

Early on Tuesday morning, Israel's defence minister, Israel Katz, wrote on X, "Gaza is burning" and threatened that Israel, "will not relent and we will not go back - until the completion of the mission."

Local journalists in Gaza say there have been almost constant Israeli air strikes and artillery and gunfire in Gaza City. Homes are said to have been destroyed, with people trapped in the rubble. There has been no official confirmation of a new ground incursion from the Israeli military.

Israel has demanded that Gaza City's residents leave and head south to a central area of the strip. The Israel Defense Forces (IDF) estimate about 250,000 Palestinians have fled, though hundreds of thousands are believed to remain in the area.

Some say they cannot afford to go south, while others say southern Gaza is not safe as Israel has carried out air strikes there too. Some have said they attempted to go south but were unable to pitch their tents, so returned to Gaza City.

Rubio meanwhile was heading to visit Qatar next, where Arab leaders on Monday condemned Israel's attack last week on the capital Doha targeting, but reportedly failing to kill, Hamas leaders.

Speaking from the tarmac at Ben Gurion airport, Rubio said Qatar was still the only country able to mediate on Gaza. Pressed by the BBC on the condemnation of Israel from Arab and Muslim countries in Doha on Monday, he said the US prefers that war ends in a negotiated settlement and hoped partners in the region "stay engaged".

Rubio also said that there was "a very short window" in which a deal on Gaza could be made, Reuters and AFP reported. He added that Hamas had to "cease to exist as an armed group".

In Israel, hostage families camped outside the Israeli prime minister's house overnight because they believe the current military strategy is putting their loved ones in danger. Some 48 hostages are believed to remain in Gaza with 20 believed to be alive.

The escalation in bombardment on Gaza also comes after Netanyahu refused to rule out further strikes on Hamas leaders abroad despite international criticism of the attack on Qatar.

Days earlier the White House said Trump had assured Qatar "that such a thing will not happen again on their soil" - an assertion that he repeated on Monday night.

Qatar hosts a major US airbase and has played a key role in brokering diplomatic efforts to end the war in Gaza, serving as a mediator of indirect negotiations between Hamas and Israel. It has hosted the Hamas political bureau since 2012.(BBC)