“I am not of the idea that he is being blackmailed,” said Nina L. Khrushcheva, a professor of international affairs at the New School in New York, currently in Moscow. “Undermining NATO and undermining Europe is something that Putin would like to do, but Trump is doing it for different reasons.”

Still, even if convinced that Mr. Trump is not being blackmailed, analysts are still puzzled over why his actions so closely coincided with Russia’s foreign policy goals.

“Once again we see a president who appears to be acting impulsively and erratically — except when it comes to Russia,” said Leslie Vinjamuri, professor of international relations at SOAS University of London. “Here, Trump has been eerily consistent in his willingness to adopt policies that enable Russia’s strategy while undermining ours.”

Nevertheless, not everything is flowing in Moscow’s favor.

“Trump’s announcement that they are leaving Syria is a gift, of course,” said Valery D. Solovei, a political-science professor at the Moscow State Institute of International Relations. The Kremlin may use its success in Syria to forge on into Libya for similar reasons, he said.

Afghanistan was more complicated, however.

“On the one hand, the Russians are gleeful about the American withdrawal; there is this ‘We told you so’ feeling,” he said, referring to the Soviet Union’s disastrous invasion of Afghanistan in 1979. But “the Kremlin has always feared that destabilization in Afghanistan could increase the flow of drugs and extremists to Russia.”

In Syria, the American presence had proved to be a convenient excuse for Mr. Putin about why the Russian intervention was not bringing the conflict to as rapid a close as he had promised. In addition, fighting the remnants of the Islamic State will now become Russia’s problem, with any upsurge in violence likely to undermine the Kremlin position that Syria is stable enough for a postwar political process and reconstruction funds.

On the sanctions front, although the United States lifted penalties on Rusal, that came at the cost of diminishing Mr. Deripaska’s role with the company. And Mr. Deripaska himself remains under sanctions for his business practices.