The two statements appeared to be business as usual — each side representing enemy No. 1 for the other, as they have since World War II ended and the Cold War began.
By Friday that mood had been abruptly cast aside, however. President Vladimir V. Putin announced that Russia would do nothing in response to the new American measures, awaiting the next administration, prompting President-elect Donald J. Trump to call him “very smart” in a Twitter post.
Russian-American relations are passing through one of their most confusing moments in modern history amid the transition from one presidential administration to the next, with the sitting president calling Russia a national security threat and the incoming one praising Mr. Putin.
With Mr. Trump making admiring remarks about Mr. Putin, without the support of Congress, many American voters, accustomed for generations to be suspicious about Russia, are understandably confused and uneasy. Russia was an enemy on Friday morning, and a friend by the afternoon.
“We are in a whiplash moment right now, and I think it is unprecedented in several respects,” said Cliff Kupchan, the chairman of the Eurasia Group, a political risk assessment firm in Washington, and a former State Department official from the Clinton administration. “The most important one is that the baton is about to be passed from an administration with a very hard line on Russia to one that is very much more sympathetic.”
No clear agreements or even offers are on the table yet, however, bringing uncertainty. “Russia’s relations with the U.S. are currently up in the air — both sides have no clear strategy about how to move them forward,” said Aleksandr Morozov, an independent Russian political analyst.
Until the Soviet Union collapsed in 1991, and even for years afterward, matters were more black and white. A young American diplomat stationed in Moscow named George F. Kennan established the parameters of the relationship for decades with a famous 1947 policy paper. The Soviet Union was bent on expansion, he wrote, so the main element of any United States policy had to be containment.
Thus began a long roller coaster ride for the two countries, full of periodic upswings as friends when détente was in vogue, inevitably followed by precipitous plummets as foes that left the world shuddering about the prospects of a nuclear Armageddon.
Tensions eased periodically, but it never seemed to last.
President Ronald Reagan, an implacable anti-Communist, surprised the world by reaching out to the man who turned out to be the last leader of the Soviet Union, Mikhail Gorbachev, to begin negotiations for far-reaching arms control agreements between the two sides.
After the Soviet Union collapsed in 1991, the Russian Federation that emerged entered into an extended period of decline and, inevitably, friendship with the United States as a kind of junior partner.
That “junior” aspect rankled, however, particular after Mr. Obama went from seeking to reset relations to dismissing Russia as a “regional power.”
The latest crisis began in 2014, with a revolution in Ukraine that Mr. Putin labeled an American plot — he, as many Soviet leaders did, sees the hidden hand of Washington everywhere. Mr. Putin annexed Crimea and armed rebels in eastern Ukraine, prompting Western economic sanctions, which Mr. Trump has disparaged.
The last confrontation under the Obama administration between Moscow and Washington came to a head this fall after American intelligence agencies concluded that hacking by their Russian counterparts had breached national security, cracking open the computers of the Democratic National Committee to reveal emails that embarrassed Hillary Clinton’s campaign. Mr. Trump initially encouraged the Kremlin to hack even more, breaking with all precedents, not least the Republican tradition of painting Russia as the evil empire, as Mr. Reagan called it.
Mr. Obama waited to react until last week, and it looked as if he might leave his successor a diplomatic tempest, until Mr. Putin, long the master of the unexpected stroke, defused it.
Mr. Trump suddenly gained room to maneuver.
“Trump’s spirit is already here, and already changing Russia’s policies,” said Igor M. Bunin, the director of the Center for Political Technologies, a Moscow research institute. “This will be a great plus for future relations.”
There are still potential pitfalls, however, not least that Congress does not share an affectionate view of Mr. Putin.
Senator John McCain, Republican of Arizona, plans to open hearings on Thursday on Russia’s efforts to manipulate the presidential election. Much of the Republican establishment in Congress endorsed the new sanctions imposed against Russia, putting them at odds with Mr. Trump.
Senator Amy Klobuchar, Democrat of Minnesota, was with Mr. McCain and Senator Lindsey Graham of South Carolina, a Republican, last week to tour the Baltic States, which fear being the next target of the Russian military.
“The Russian cyberattack, and the misinformation and propaganda — they have been living with this for decades,” Ms. Klobuchar said in an interview.
American voters have heard Mr. Trump praise Russia, and some in the far right have hailed Mr. Putin as a hero for espousing conservative values. Yet old instincts die hard.
“I worry about what our relationship with other countries is going to be with a Trump presidency, if we buddy-buddy up to Russia and a leader who is not so democratic in nature,” said Alexis Matter, 35, walking through a Denver shopping mall.
In Sandy Springs, Ga., Chase Williams, 26, the manager of a pet supply store, acknowledged that Russia had fallen off the radar in recent years. His fears now were less of the old Cold War over a nuclear weapons attack than a sense that Mr. Putin could outfox the American administration.
“When I say Russia scares me, it’s not because I’m scared of them coming over here and doing something,” Mr. Williams said. “I’m scared when I see a chess player playing checkers — and we are checkers.”
Mr. Putin has made no secret of the fact that he would like to re-establish the consensus reached with the United States at the 1945 Yalta conference that carved the globe into spheres of influence.
Russia no longer has the might needed to assert its right to be a superpower, analysts say, but if nothing else, cyberattacks have underscored that you do not need nuclear weapons or a strong economy to assert global influence.
Some Russian analysts wonder what Mr. Putin can offer Mr. Trump. A former K.G.B. agent, he tends to view the world order as a series of special operations, coming from a different arena than Mr. Trump’s world of business deals. “I don’t think that Putin has a plan,” said Gleb Pavlovsky, a political analyst and former media adviser to Mr. Putin. “I think that he is stunned by the number of bonus points that he has gotten.”
In Syria, President Bashar al-Assad is on the verge of reasserting control over much of the country, thanks largely to Mr. Putin’s intervention. Ukraine presents some problems, but has essentially boiled down into the kind of frozen conflict that Russia uses to destabilize independent-minded neighbors. And all of the attention on the cyberattacks made Mr. Putin look strong.
In those successes, analysts see the fodder for Mr. Putin to offer Mr. Trump a manner of foreign policy success that would give the American leader something tangible to crow about at home in an arena where he lacks experience.
Russia, Iran and Turkey cut Washington out of the Syria negotiations, so Mr. Putin could bring the United States back in and forge a deal on fighting the Islamic State. Mr. Trump has stated that he wants to join forces with Russia in crushing the jihadists. Or the Kremlin could offer some manner of cyberspace deal.
“I think that Putin is in a strong position,” said Nicolai Petrov, a Russian political scientist. “He looks strong in relation to the United States and he has freedom to maneuver, and he can do what he wants to demonstrate that the United States should recognize that Russia is not a regional power but a great power that should be taken into account.”
So, for the moment, Mr. Putin appears a potential friend to Mr. Trump.
Few expect it to last, however. First of all, Mr. Trump is unpredictable. Fundamentally, the two countries are destined to be at odds, because they view the world through different lenses.
Russian policy in recent years has been trying to sow doubt and undermine public faith in Western governments. The Kremlin has relied on a variety of levers — disinformation campaigns, buying influence, cyberattacks — which many analysts expect to show up in crucial elections expected this year in France and Germany.
“They are trying to create more of a level playing field not by raising Russia up, but through a declining West,” Mr. Kupchan said. “I don’t think Putin is out to make America great again.”