In the last week, Mr. Trump has written on Twitter that the United States “must greatly strengthen and expand its nuclear capability”; accused China of an “unprecedented act” in seizing a United States Navy underwater drone in the South China Sea; and then, after the Pentagon and the Chinese negotiated the drone’s return, suggested that the United States should “let them keep it!”

He condemned the deadly truck rampage at a Christmas market in Berlin as an “attack on humanity,” which he also said vindicated his proposed ban on immigration from countries plagued by Islamic extremism. On Friday, Mr. Trump wrote in a Twitter post that the suspect in the attack had made a religiously motivated threat. “When will the U.S., and all countries, fight back?” he wrote.

Mr. Trump’s pronouncements are often so vague and offhand that their long-term impact on policy is open to debate. But his intervention to press Egypt to delay the Security Council vote disrupted a sensitive diplomatic negotiation, and muddied perhaps Mr. Obama’s final opportunity to make a statement on the stalled Middle East peace process.

When Egypt buckled, the same resolution was brought to a vote by four other countries on the Security Council: Malaysia, New Zealand, Senegal and Venezuela. The United States watched the proceedings largely from the sidelines. On Friday morning, Mr. Obama, from his vacation home in Hawaii, directed his national security adviser, Susan E. Rice, to tell the ambassador to the United Nations, Samantha Power, not to block the resolution.

“In a practical sense, the message this sends is that the Obama administration is over,” said Daniel C. Kurtzer, a former American ambassador to both Egypt and Israel. “Everybody knows this resolution doesn’t carry any weight. The assumption has to be that the Israeli government will take some retaliatory measures. Knowing that Trump is coming into office, and knowing that Trump tried to oppose this, they will do so with impunity.”

This role reversal between the departing and incoming presidents deepened what was already an unsettled moment in American foreign policy: a sense that the White House’s policies toward the world’s most troubled places had run out of steam and were about to change radically, but in ways that were wholly unpredictable.

Mr. Trump has been careful to be respectful of his predecessor, and the president-elect’s aides have said that the two men have spoken often. When people at his rallies jeer at the mention of Mr. Obama’s name, Mr. Trump hushes them — a courtesy he does not extend to his former opponent, Hillary Clinton. But Mr. Trump has shown little patience for the traditions of the interregnum between presidents.