Secretary of State Antony J. Blinken said on Wednesday that he would continue to press urgently for a cease-fire deal between Israel and Hamas in the Gaza Strip despite a counterproposal from Hamas that he said included unacceptable demands.

After more than eight months of war in Gaza, the proposed cease-fire deal follows an outline made public last month by President Biden and has the endorsement of the United Nations Security Council. But Israel and Hamas still appear to be far from reaching a deal.

“In the days ahead, we are going to push on an urgent basis,” Mr. Blinken said, “to try and close this deal.”

Speaking at a news conference in Doha, Qatar, alongside Mohammed bin Abdulrahman Al Thani, who serves as both Qatar’s prime minister and minister of foreign affairs, Mr. Blinken said that “a deal was on the table that was virtually identical” to one that Hamas put forward on May 6.

But Hamas’s response, he said, which was received by Egyptian and Qatari mediators and passed to American officials on Tuesday, makes demands that “go beyond positions that it had previously taken and accepted.”

“Some of the changes are workable, some are not,” Mr. Blinken said. He declined to disclose details about the Hamas counterproposal but suggested that the group’s changing demands called into question its negotiators’ sincerity. At some point, he said, “you have to question whether they’re proceeding in good faith or not.”