Israel and Hamas have made some progress toward agreement on a 30-day ceasefire in Gaza when Israeli hostages and Palestinian prisoners would be released, sources told Reuters, as Israel pressed ahead with its assault on southern Gaza's main city.

Qatar, the U.S. and Egypt have for weeks shuttled between Israel and the militant group that runs Gaza trying to broker terms for a break in fighting, which would also allow in more food and medical supplies.

But the two sides remain at odds over how to permanently end the Gaza war, and Hamas has refused to move forward until this is resolved, the sources said.

Israeli spokesperson Eylon Levy said on Tuesday there would be no ceasefire that left Hamas in power and hostages in Gaza, following the militant group's cross-border rampage on Oct. 7 in which some 1,200 Israelis were killed.

Palestinian health officials say 25,490 Gazans have since been killed, with thousands more feared lost under the rubble of destroyed buildings.

The U.S. State Department and White House, Qatar's foreign ministry and Egypt's State Information Service did not immediately respond to requests for comment on prospects for a new ceasefire deal, following a week-long truce in November.

In their biggest operation in a month, Israeli forces pressed on with their capture of the city of Khan Younis, where hundreds of thousands of displaced Palestinians are sheltering after leaving the north - the early focus of the war.

Israeli tanks on Tuesday shut the road from Khan Younis towards the Mediterranean coast, blocking the escape route for civilians trying to reach Rafah on Gaza's southern edge bordering Egypt - now crammed with more than half the enclave's 2.3 million people.

The military said on Wednesday it had killed "numerous" squads of gunmen "with sniper, tank and aerial fire" in western Khan Younis, a new focus of its operations, close to the city's two main hospitals.

Israel says it has killed around 9,000 militants in total, a number Reuters cannot verify. Hamas officials dismissed Israeli figures as an attempt to "portray a fake victory".

The Palestinian Red Crescent Society said on Wednesday that three displaced individuals had been killed and two others injured at the gate of its headquarters in Khan Younis.

Gaza health ministry spokesman Ashraf Al-Qidra accused Israel of targeting the Nasser Hospital, the largest medical facility still operating, saying attacks were blocking access for medics and patients and threatening to put it out of action.

"The occupation is placing the lives of medical teams, patients, the injured and the displaced in several hospitals in Khan Younis in danger," he said.

Israel says Hamas fighters operate in and around hospitals, which hospital staff and Hamas deny.

UN AID FACILITIES UNDER ATTACK

Martin Griffiths, U.N. coordinator of emergency relief, said on Tuesday that 24 people had been killed in strikes on an aid warehouse, U.N. centre and humanitarian zone in the Khan Younis area, and that a centre where aid is distributed to families had come under heavy bombardment.

Some people were taking dirt roads out of Khan Younis to try to reach Rafah, or Deir Al-Balah to the north, according to residents and freelance reporters leaving the area.

Video footage from different areas has shown Palestinians burying their dead as best they can, in streets and markets as well as the grounds of hospitals and, more recently, inside Al-Aqsa University, west of Khan Younis.

"The entire population of Gaza is enduring destruction at a scale and speed without parallel in recent history," United Nations Secretary-General Antonio Guterres told the U.N. Security Council.

"Nothing can justify the collective punishment of the Palestinian people," he said, denouncing Israel's opposition to creation of a Palestinian state existing alongside Israel.

Diplomacy around a ceasefire deal appeared intense. Qatar said on Tuesday it had "presented ideas to both sides, we are getting a constant stream of replies from both sides, and that in its own right is a cause for optimism."

U.S. Middle East envoy Brett McGurk was in Cairo and due to hold "active" discussions on ensuring release of hostages and securing a humanitarian pause, the White House said. More than 130 hostages are still being held in Gaza, according to Israeli tallies.

Each side blamed the other for the collapse of a seven-day truce in November in which Hamas had freed women, children and foreign hostages in exchange for daily releases of Palestinians from Israeli prisons.