Fighting between Israel and Hamas intensified across Gaza on Monday, fuelling fears flagged by the UN at the weekend of a breakdown in public order and a mass exodus of Palestinians into Egypt.

The narrow coastal strip has been under a full Israeli blockade since the start of the conflict more than two months ago and the border with Egypt is the only other way out.

Most of Gaza’s 2.3 million people have been driven from their homes and they say it is impossible to find refuge in the populated enclave, with 18,000 people already killed and conflict intensifying.

Since the breakdown of a week-long ceasefire, Israel launched a ground offensive in the south last week and has since pushed from the east into the heart of the major city of Khan Younis, with warplanes attacking an area to the west.

On Monday, militants and some residents said fighters were preventing Israeli tanks moving further west through the city and there were also fierce clashes in parts of northern Gaza, where Israel had said its tasks were largely complete.

Gazans forced to flee repeatedly described desperate attacks on aid trucks, sky-high prices and said people were dying of hunger and cold as well as bombardment.

“Hunger is the base for all evils that destroy the social fabric of communities,” writer Aziz Almasri said on Facebook. “It is the second face of the war we see today in Gaza.”

Israelis fled to shelters after new warnings of rocket fire from Gaza, including in Tel Aviv. The armed wing of Hamas said it was bombarding the city in response to “the Zionist massacres against civilians”.

In the northern Gazan city of Jabalia, Palestinians ran to escape smoke bombs fired near tents and other homes and militants said they were clashing with Israeli troops.

Israeli army spokesman Avichay Adraee issued a new call on X on Monday for Gaza residents to evacuate Gaza City and other areas of the north as well as Khan Younis in the south.

UN officials say 1.9 million people — 85 per cent of Gaza’s population — are displaced and describe the conditions in the southern areas where they have concentrated as hellish.

“I expect public order to completely break down soon and an even worse situation could unfold including epidemic diseases and increased pressure for mass displacement into Egypt,” UN Secretary-General Antonio Guterres said on Sunday.

Philippe Lazzarini, the commissioner general of UNRWA, the UN body responsible for the welfare of Palestinian refugees, said the Gazans driven from their homes were being pushed closer and closer to the border.

“The developments we are witnessing point to attempts to move Palestinians into Egypt,” Lazzarini wrote in the Los Angeles Times. The border is heavily fortified, but Hamas militants blew holes in the wall in 2008 to break a tight blockade.