But they represent a determination by the 44th president to squeeze in every last Obama-era achievement before Mr. Trump — who has vowed to dismantle those achievements — takes over. That has cheered some of Mr. Obama’s liberal allies, who wish he could do even more.

“The Republicans are freaking out because all of a sudden Obama is doing a lot of governing,” said Matt Bennett, the senior vice president for public affairs at the Third Way, a liberal think tank. “They don’t like it. I get that. But he’s in his right to do it, and he should do it. Is he trying to box Trump in? You bet — and he should.”

Mr. Obama’s actions have not gone unnoticed by Mr. Trump and the people working frantically to assemble the new administration. A day after Mr. Obama allowed passage of a United Nations Security Council resolution criticizing Israeli settlements, Mr. Trump angrily wrote on Twitter that the move would “make it much harder to negotiate peace.” Mr. Trump added, optimistically: “Too bad, but we will get it done anyway!”

Two days later, in a sign of his growing frustration with Mr. Obama, Mr. Trump posted again on Twitter, saying he was doing his best to “disregard the many inflammatory President O statements and roadblocks.”

He continued, “Thought it was going to be a smooth transition — NOT!”

That Twitter message apparently prompted a phone call from Mr. Obama the next day, when the president and president-elect tried to re-emphasize their cooperation. Mr. Obama’s spokesman issued a statement calling the discussion positive, saying both men had pledged to “work together to effectuate a smooth transition of power on January 20th.”

That evening, from his Mar-a-Lago estate in Florida, Mr. Trump insisted that the transition was going “very, very smoothly” and said his talk with Mr. Obama had been a “very, very nice” conversation.

“Our staffs have been getting along very well, and I’m getting along very well with him other than a couple of statements that I responded to,” Mr. Trump said.