The Palestinian official added that the strike on the power plant might be an additional factor pushing the sides toward a cease-fire, in order to avert a crisis. The plant had been Gaza’s main source of electricity in recent days, after eight of 10 lines that run from Israel were damaged.

The Palestinian announcement seemed to be part of a larger effort involving Egypt, an important participant in any cease-fire deal for both Israel and Mr. Abbas. The Egyptian Foreign Ministry said that Mr. Abbas had initiated a proposal to bring representatives of the Palestine Liberation Organization, Hamas and Islamic Jihad to Cairo for another round of cease-fire talks, which Egypt supports.

Regarding the talks, Osama Hamdan, a Hamas official in Beirut, said: “On principle, we have no objection and accept. A delegation will be formed, and we might leave for Cairo soon.”

Israel favors Egypt as a broker, and Prime Minister Benjamin Netanyahu has described Egypt’s original proposal for a cease-fire, which Israel accepted and Hamas rejected, as “the only game in town.”

In Washington, Secretary of State John Kerry signaled Tuesday that the Obama administration had not abandoned its hope of arranging a cease-fire. Mr. Kerry emphasized that Mr. Netanyahu had told him on Monday that he might accept a truce if it would allow Israeli forces to continue to operate against Hamas’s tunnels, some of which run under the border into Israeli territory and have been used for attacks.

“Last night we talked, and the prime minister talked to me about an idea and a possibility of a cease-fire — he raised it with me, as he has consistently,” Mr. Kerry said at a news conference with his Ukrainian counterpart, Pavlo Klimkin. “He has consistently said that he would embrace a cease-fire that permits Israel to protect itself against the tunnels and obviously not be disadvantaged for the great sacrifice that they had made in order to be able to protect themselves thus far.”