Prime Minister Benjamin Netanyahu of Israel called Hamas’s response to the latest peace proposal for Gaza “negative.” Hamas insisted it was dealing with it “positively.”

Secretary of State Antony J. Blinken, speaking in Qatar, said Hamas had demanded changes, some of which were “workable” and some not. A Hamas official told an Arabic television channel that the group had not raised any new ideas, and that Mr. Blinken saw things through an Israeli lens and “speaks Hebrew.”

The Biden administration has pledged to keep working with the Qatari and Egyptian mediators to bridge the gaps. But after days of intensive diplomacy in the region, a monthslong effort to end the war in Gaza seems as stuck as ever, as each side clings stubbornly to maximalist demands unacceptable to the other.

Asked at the Group of 7 summit meeting in Italy if he still thought a deal could be reached, President Biden said, “I haven’t lost hope, but it’s going to be tough.”

At the crux of the disagreement over the three-phased deal, according to officials and experts, is Hamas’s goal of essentially securing a permanent cease-fire from the outset and a withdrawal of all Israeli troops from Gaza before handing over most of the hostages.

Israel says it is willing to negotiate a permanent cessation of the war, now in its ninth month — but only after dismantling Hamas’s military and governing capabilities. That clashes with Hamas’s goals of surviving the war and retaining control of the coastal enclave.