Mediator Egypt has presented a new Israeli proposal for a Gaza ceasefire to Hamas, Egyptian state-affiliated Al Qahera News TV says.
However, a senior Hamas official said at least two elements of the proposal were non-starters.
Citing sources, Al Qahera said mediators awaited Hamas' response. But senior Hamas official Sami Abu Zuhri's assessment suggested the militant group was unlikely to agree.
Abu Zuhri told Reuters the proposal did not meet the Palestinian group's core demand that Israel commit to a complete halt of hostilities.
In the proposal, Israel also for the first time called for the disarmament of Hamas in the next phase of negotiations, which the militant group will not agree to, Abu Zuhri said on Monday.
"Handing over the resistance's weapons is a million red lines and is not subject to consideration, let alone discussion", Abu Zuhri said.
Israel restarted its offensive in the enclave in March, ending a ceasefire that went into effect in late January.
The latest round of talks on Monday in Cairo to restore the ceasefire and free Israeli hostages ended with no apparent breakthrough, Palestinian and Egyptian sources said.
Hamas insists Israel commit to ending the war and pull out its forces from the Gaza Strip as agreed in the three-phase ceasefire accord that went into effect in late January.
Israel has said it will not end the war unless Hamas is eliminated and returns the remaining hostages held in Gaza.
"Hamas is ready to hand over the hostages in one batch in exchange for the end of war and the withdrawal of Israeli military" from Gaza, Abu Zuhri said.
Since restarting its military campaign last month, Israeli forces have killed more than 1500 Palestinians, Gaza health authorities have said. It has displaced hundreds of thousands of people and imposed a blockade on all supplies entering the enclave.
Meanwhile, 59 Israeli hostages remain in the hands of the militants. Israel believes 24 of them are alive.
