The United Nations Security Council on Monday adopted a U.S.-backed cease-fire plan for the Gaza Strip with only Russia abstaining, a sign of the growing frustration among the world’s major powers over the war and the desire to bring it to an end.

Linda Thomas-Greenfield, the U.S. ambassador to the United Nations, told members of the Security Council that Israel had already agreed to the deal laid out in the resolution — although Israel has so far resisted taking a public position on it — and she urged Hamas “to do the same.”

“Hamas can now see that the international community is united, united behind a deal that will save lives and help Palestinian civilians in Gaza start to rebuild and heal,” Ms. Thomas-Greenfield said.

The 14-0 vote may strengthen the hand of Secretary of State Antony J. Blinken, who returned to the Middle East on Monday to press Hamas and Israel to agree to a cease-fire.

But in a sign of the difficulties facing Mr. Blinken and other mediators in achieving a final deal, Israel’s representative to the U.N., Reut Shapir Ben-Naftaly, did not say that Israel had accepted the terms of the cease-fire plan. She said that her country’s goals in the war had not changed and that it would use military operations to free hostages, as it did just two days ago.

“We will continue until all of the hostages are returned and Hamas’s military capabilities are dismantled,” Ms. Shapir Ben-Naftaly told the Council. She said if Hamas leaders freed all hostages and turned themselves in, “not one shot would be fired.”