President-elect Donald Trump and President Barack Obama have been unfailingly polite toward each other since the election. But with Trump staking out starkly different positions from Obama on Israel and other sensitive issues, and the president acting aggressively to protect his legacy, the two have become leaders of what amounts to dueling administrations.

The split widened Friday when the Obama administration abstained from a United Nations Security Council vote condemning Israel for Jewish settlements in the West Bank, and allowed the resolution to pass. A day earlier, Trump had publicly demanded Obama veto the measure, even intervening with Egypt at the request of Israel to pressure the administration to shelve the effort.

"As to the U.N.," Trump wrote on Twitter after the vote, "things will be different after Jan. 20th."

It was the latest in a rapid-fire series of Twitter posts and public statements over the last week in which Trump has weighed in on Israel, terrorism and nuclear proliferation – contradicting Obama and flouting the notion the country can have only one president at a time.

That long-standing principle has largely collapsed since the victory by Trump, who campaigned on a strategy of breaking all the rules and has continued to speak in unmodulated tones.

"In some ways, Trump is neutering the Obama administration," professor of history and presidential historian at Houston's Rice University Douglas Brinkley Douglas Brinkley. "They've avoided personally attacking each other, but behind the scenes, they're working to undermine each other, and I don't know how the American people benefit from that."

For its part, the Obama administration on Tuesday announced a permanent ban on offshore oil and gas drilling along wide areas of the Arctic and the Eastern Seaboard, invoking an obscure provision of a 1953 law, the Outer Continental Shelf Lands Act, to claim Trump had no power to reverse it.

White House officials asserted a similar privilege in their decision not to veto the Security Council resolution. Israel's aggressive construction of settlements in the West Bank and East Jerusalem, they said, puts at risk a two-state solution to the Israeli-Palestinian conflict. Trump's opposition to the measure, and the likelihood his administration will reverse the position, played no part in the decision, they said.

"There's one president at a time," deputy national security adviser Benjamin Rhodes said. "There's a principle here that the world understands who is speaking for the United States until January 20th, and who is speaking for the United States after January 20th."

In the last week, Trump has written on Twitter the United States "must greatly strengthen and expand its nuclear capability"; accused China of an "unprecedented act" in seizing a U.S. Navy underwater drone in the South China Sea; and then, after the Pentagon and the Chinese negotiated the drone's return, suggested 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, Trump wrote in a Twitter post the suspect in the attack had made a religiously motivated threat. "When will the U.S., and all countries, fight back?" he wrote.

Trump's pronouncements are often so vague and offhand 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 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, Obama, from his vacation home in Hawaii, directed his national security adviser, Susan 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 Kurtzer, a former U.S. 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 U.S. 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.

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

"President Obama and his team have been unbelievably gracious to the president-elect and his team, but at the end of the day, he's not someone that's going to sit back and wait," Sean Spicer, whom Trump named Thursday as White House press secretary, said on CNN.

Noting the close alliance between Israel and the United States, Spicer said, "It is something that we should protect, and he wanted to make it very clear that anything that undermined Israel, which is a great friend of the United States, he was going to make sure his voice was heard."

It is not unprecedented for future presidents to dip into foreign affairs before taking office. During his transition in 1968, Richard Nixon dispatched two aides, Henry Kissinger and Robert Ellsworth, to meet with Soviet officials to pass along his views on a nonproliferation treaty and a summit meeting, an idea that was being pushed by President Lyndon B. Johnson.

Nixon later wrote that he "did not want to be boxed in by any decisions that were made" before he took office.

More often, though, incoming presidents have been hands-off. In December 1932, the departing president, Herbert Hoover, was deeply frustrated when Franklin D. Roosevelt, who had won a landslide victory a month earlier, declined to work with him on the issue of war debts owed to the United States by Britain and France. "Gov. Roosevelt considers it undesirable for him to assent to my suggestions for cooperative action," he said.

Eliot Cohen, a Republican foreign policy expert who worked in the George W. Bush administration and is a critic of Trump, said the president-elect was still communicating in the style of a political candidate.

"I don't think he has a good sense of how every word that comes out of his mouth can have real consequences," he said.

Whatever their frustrations about his interference, White House officials were careful not to criticise Trump after the Security Council vote. And in his Twitter message promising change at the United Nations, Trump pointedly did not criticise Obama or his administration.

Still, Trump has shown no sign he will surrender his Twitter account or curb his public statements in the next 28 days, which could lead to more mixed messages and tension with the White House. Experts have said Trump would do well to follow the example of his reticent predecessors.

"This is not politesse," presidential historian Michael Beschloss said. "Even a president-elect who has been in public life for a long time has not been fully briefed or fully staffed, and hence may be in a position to do this better once he's in the White House."

"What's the rush?" he said.