Smoke billows over Khan Yunis in the southern Gaza Strip during Israeli bombardment on Monday. AFP

Combat raged in Khan Yunis in the southern Gaza Strip on Tuesday, against a backdrop of negotiations aimed at bringing about a pause in fighting between Israel and Hamas in the absence of a long-term peace plan.

The Palestine Red Crescent Society said early on Tuesday that Israeli forces had targeted its headquarters in Khan Yunis "with artillery shelling on the fourth floor, coinciding with intense gunfire from Israeli drones, resulting in injuries among internally displaced individuals who sought safety on our premises".

The UN humanitarian agency OCHA reported that "ground operations, fighting and attacks intensified" over the preceding day around the main southern city, with the Israeli army saying its forces had conducted multiple raids and taken control of Hamas command centres there.

The fierce fighting came as a White House official was due in the region for talks aimed at securing more hostage releases, and as US media reported a new Israeli proposal for a deal that would involve a two-month pause in fighting.

UN agencies and aid groups have sounded the alarm about the growing threat of disease and famine in Gaza, where 1.7 million people are estimated to have been displaced from their homes.

Abu Iyad, his belongings piled on a donkey-drawn cart, told the media on Monday that he was moving for the seventh time, fleeing Khan Yunis for Rafah on the Egyptian border, where hundreds of thousands of displaced Palestinians have settled, many in makeshift tents.

"I'm heading to the unknown," he said. "They told us to go to Rafah -- where to go in Rafah? Is there any space left?"

Hostage talks

Israel has carried out a relentless offensive that has killed at least 25,295 people in Gaza, around 70 per cent of them women, children and adolescents, according to Gaza's health ministry.

The Hamas attack also saw about 250 hostages seized, and Israel says around 132 remain in Gaza. That number includes the bodies of at least 28 dead hostages, according to an AFP tally based on Israeli data.

Relatives of the captives stormed a parliamentary committee meeting on Monday demanding urgent action.

"You sit here while our children are dying over there," yelled Gilad Korngold, father of hostage Tal Shoham, an AFP correspondent reported.

US news outlet Axios reported on Monday night that Israel had proposed to Hamas, via Qatari and Egyptian mediators, a new deal to free all the hostages.

The report, citing unnamed Israeli officials, said the proposed deal would be carried out in multiple stages, and would also involve the release of an undetermined number of Palestinian prisoners.

The plan was expected to take about two months to complete.

The proposal does not include promises to end the war, but it would involve Israeli troops reducing their presence in major cities in Gaza and gradually allowing residents to return to the territory's devastated north, the Axios report said.

News of the proposal comes as US media said the White House's coordinator for the Middle East, Brett McGurk, was expected in Egypt and Qatar for meetings aimed at securing a new hostage exchange deal.

State Department spokesman Vedant Patel, however, said that Washington still believed "a two-state solution, a creation of a Palestinian state, is the only path that gets us out of this endless cycle of violence".

Agence France-Presse