Israel pressed on with its bombing of Gaza on Tuesday after saying its campaign to destroy Hamas has left the Palestinian militant group on the "the verge of dissolution".

Humanitarian leaders fear the besieged territory will soon be overwhelmed by disease and starvation, and are piling diplomatic pressure on Israel to boost efforts to protect civilians.

Fighting raged on Tuesday, with Hamas saying clashes had taken place in central Gaza and witnesses reporting deadly Israeli strikes in the south of the territory.

Israeli air strikes killed at least 12 people in the southern city of Rafah near the border with Egypt, where tens of thousands of people are seeking shelter, official Palestinian news agency Wafa said.

Strikes on Monday targeted Gaza's main southern city of Khan Yunis, now the epicenter of the fighting.

"Hamas is on the verge of dissolution — the IDF is taking over its last strongholds," Israeli Defense Minister Yoav Gallant said late Monday.

The war began with Hamas's 7 October attacks that killed 1,200 people, according to Israeli figures, and saw around 240 hostages taken back to Gaza.

Israel has responded with an offensive that has reduced much of Gaza to rubble and killed at least 18,200 people, mostly women and children, according to the Hamas-run health ministry.

Israel's army chief Herzi Halevi on Monday visited the centre of Khan Yunis, where he said his forces were "securing our accomplishments in the northern part of the Gaza Strip, the entrance in the southern part of the Strip, and also deep down into the ground".

The UN estimates 1.9 million of the territory's 2.4 million people have been displaced by the war, half of them children.

Fighting and heavy bombardment in the south, where Israel had previously urged civilians to seek safety, have left people with few places to go.

Umm Mohammed al-Jabri lost seven children in an air strike on Rafah after fleeing there from Gaza City further north.

"I have four children left," said Jabri, 56. "Last night they bombed the house we were in and destroyed it. They said Rafah would be a safe place. There is no safe place."

'No bread, no milk'

Civilians in Gaza are facing a catastrophic situation, the EU's top diplomat Josep Borrell said Monday, comparing the territory's destruction to that of Germany during World War II.

Health services have been devastated, with only 14 of Gaza's 36 hospitals functioning at any capacity, according to UN humanitarian agency OCHA.

In central Gaza, Al-Aqsa hospital was inundated with victims Monday, including dozens of screaming children, after Israeli strikes on the Al-Maghazi refugee camp.

As basic supplies run out and sanitary conditions deteriorate, women and girls in Rafah said they had been forced to use scraps of cloth for menstrual periods.

"I cut up my kid's clothes or any piece of cloth I find," said 25-year-old Hala Ataya.

In Gaza City, thousands of Palestinians set up camp at a UN agency headquarters after nearby homes and shops were destroyed by Israeli strikes.

An AFP correspondent said both the Islamic and adjacent Al-Azhar universities had been reduced to rubble, as had the police station.

"There is no water. There is no electricity, no bread, no milk for the children, and no diapers," said Rami al-Dahduh, 23, a tailor.

International aid organisations have struggled to get supplies to desperate Gazans under Israeli bombardment, with only the Rafah crossing in Egypt open.

Facing growing pressure to do more for civilians, Israel announced Monday it would be screening aid to Gaza at two additional checkpoints, which would allow more assistance to enter the ravaged territory.

No new direct crossings will be opened, Israel said, but the Nitzana and Kerem Shalom crossings will be used to carry out checks before sending the trucks through Rafah.

UN vote

The UN General Assembly is due to vote Tuesday on a non-binding resolution demanding "an immediate humanitarian ceasefire" in Gaza — a call that the Security Council has so far failed to make.

The United States, one of only five permanent members of the Security Council, used its veto on Friday to halt a draft text calling for a ceasefire.

In a bid to build pressure, Arab countries called for the new special session of the General Assembly following a visit to the Rafah border by more than a dozen Security Council ambassadors.

The draft text, seen by AFP, largely reproduces the resolution blocked in the Council on Friday by the United States.

Fears of a wider conflict continue to grow, with Iran-backed groups targeting US and allied forces in Iraq and Syria, and daily exchanges of fire along Israel's border with Lebanon.

The US military said a missile launched by Iran-backed Huthi rebels struck a Norwegian-flagged tanker off Yemen on Tuesday, but no casualties were immediately reported.

A drone and rockets targeted two military bases in Iraq and Syria on Monday housing forces of the international coalition against the Islamic State group, a US military official said.

Israeli bombardment killed an official in south Lebanon, the National News Agency said, amid near-daily cross-border exchanges between Israel and Hezbollah.

Israel has observed "heightened aggression and increased attacks by Iranian-backed Hezbolllah", war cabinet member Benny Gantz said Monday, vowing "to remove such threat from the civilian population of northern Israel".

In the Israeli-occupied West Bank and Lebanon, a general strike in solidarity with Gaza saw shops, schools and government offices closed on Monday.