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 US and Egypt have for weeks shuttled between Israel and Hamas 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, which Hamas insists must be decided as part of any ceasefire agreement, 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 group's cross-border rampage on October 7 in which some 1,200 Israelis were killed.
And the White House reiterated its insistence that Gaza's future government could not include Hamas leaders, prompting Hamas to say it would not let the US or anyone else "enforce a mandate on our free people".
White House spokesperson John Kirby said the US would support a pause in combat to free hostages and let aid in, but gave no timeframe and said he would not call the discussions "negotiations".
Qatar and Egypt did not immediately respond to requests for comment.
Palestinian health officials said at least 25,700 Gazans had been killed in the war, including 210 in the previous 24 hours, with thousands more feared lost under the rubble of destroyed buildings.
In their biggest operation in a month, Israeli tanks have pushed through the city of Khan Younis, where hundreds of thousands of displaced Palestinians are sheltering after leaving the north - the early focus of the war.
On Tuesday, the Israeli military ordered the evacuation of an area that the United Nations humanitarian office said was inhabited by half a million people while also shutting off the road from the city towards the Mediterranean coast.
The road was the main escape route for civilians trying to reach Rafah on Gaza's southern edge bordering Egypt - already crammed with more than half the enclave's 2.3 million people. Some people from Khan Younis resorted to dirt roads to try to escape, residents and freelance reporters leaving the area said.
Residents reported fierce gunbattles in the west of the city, where the military said it had killed "numerous" squads of gunmen "with sniper, tank and aerial fire" in the area, which is close to its two main hospitals.
Israel says it has killed around 9,000 militants in total, a figure that Hamas dismisses as an attempt to "portray a fake victory".