Mr. Netanyahu cited that history on Thursday. “I hope the U.S. won’t abandon this policy,” he said. “I hope it will abide by the principles set by President Obama himself in his speech in the U.N. in 2011 — that peace will come not through U.N. resolutions, but only through direct negotiations between the parties.”

Frustrated by two failed efforts to broker peace between Israelis and Palestinians during his tenure, Mr. Obama has been considering an effort to lay out an American framework during his final days in office. Palestinian leaders and their allies had hoped he would allow the anti-settlement resolution at the United Nations to pass as an expression of frustration at Israeli policies.

A Palestinian delegation traveled to Washington this month to urge Mr. Obama’s team to support the anti-settlement resolution or at least abstain. Mr. Obama’s advisers did not disclose a position and were holding out until the vote to watch how the matter developed. The Palestinians were unable to meet with Mr. Trump’s aides and expressed disappointment on Thursday with his position. “A veto means support of settlement activities,” Saeb Erekat, the Palestinian negotiator, said after the resolution was pulled. “A veto means abandoning the two-state solution and peace efforts.”

Asked about Mr. Trump’s comments, a visibly upset Palestinian ambassador to the United Nations, Riyad Mansour, said, “He is acting on behalf of Netanyahu.”

The return of the Palestinian cause to the world stage could serve the interests of some Arab leaders eager to turn public attention away from troubles at home. The government of Mr. Sisi, which sponsored the resolution as the Arab representative on the Security Council, faces domestic challenges stemming from a deteriorating economy, a persistent Islamic terrorist insurgency and this month’s bombing of a Coptic Christian cathedral.

At the same time, it could distract from Mr. Netanyahu’s efforts to forge stronger relations with Sunni Arab nations on the basis of shared antipathy toward Iran, dominated by a Shiite theocracy that has threatened Israel’s existence and challenged Arab interests in the region. Arab leaders, who have largely overlooked the Palestinian issue in recent years, may feel pressured to distance themselves from Israel again if their own publics are angered at the treatment of Palestinians.

Egypt backed off on the resolution after Mr. Netanyahu’s government put pressure on Mr. Sisi’s government to withdraw it, shortly before Arab ambassadors meeting at the United Nations endorsed it.