Hamas said it would head to Cairo on Saturday to meet with mediators ahead of a new round of Gaza cease-fire talks, as the United States, Qatar and Egypt push to reach an agreement they hope can stave off the growing threat of regional war.

The fighting in Gaza has raged on even as high-stakes efforts for a deal intensify, with Israeli strikes overnight killing dozens, according to the Civil Defense emergency service in Gaza. On Friday, the Israeli military announced that at least one soldier had been killed and several others were wounded in fighting in central Gaza.

While U.S. officials have insisted there is progress in negotiations, the main warring parties, Israel and Hamas, have been far more pessimistic in their assessment. In late July, Benjamin Netanyahu, the Israeli prime minister, stiffened Israel’s position on several key issues, including by demanding a postwar Israeli presence along Gaza’s border with Egypt.

Negotiators have been pushing for a major summit as early as Sunday to move ahead with the talks. Hamas said on Saturday that a delegation of its representatives would arrive in Cairo that evening to “hear the results” of a recent round of discussions between Israel, Egypt and the United States.

In a statement, the group said it was willing to move ahead with a proposal from early July, before Mr. Netanyahu set out his new conditions.

Hamas did not specifically say whether it would participate in a summit next week; its officials did not join a similar round of talks in Qatar earlier this month, calling it pointless given the new Israeli demands. But the visit to Cairo leaves the door open for further talks.