WASHINGTON — When President Biden declared to reporters on Wednesday, almost off the cuff, that President Vladimir V. Putin was a “war criminal,” he was speaking from the heart, his aides said, reacting to the wrenching images of civilians — including children — being dragged, dead or disfigured, from ruins of buildings shelled by Russian forces.

But he was also personalizing the conflict, in a way past presidents have avoided at moments of crisis with the United States’ leading nuclear-armed adversary for most of the past 75 years. And his remark underscored how personal condemnation has become policy, as Mr. Biden and his top aides frame Mr. Putin to Americans, Russians and the world as a pariah, an indiscriminate killer who should be standing trial at The Hague instead of running a faded superpower.

Mr. Biden amplified his attacks on Thursday, calling Mr. Putin “a murderous dictator, a pure thug who is waging an immoral war against the people of Ukraine.” His secretary of state, Antony J. Blinken, chimed in as well, saying: “Personally, I agree. Intentionally targeting civilians is a war crime.”

But what began as a visceral reaction by Mr. Biden also appears to reflect a strategic decision that branding Mr. Putin as a war criminal supports the administration’s case as it simultaneously tries to keep the Western alliance unified — amid differing views in Europe over the wisdom of cornering the Russian leader and leaving him with no way out of the conflict — and attempts to pressure China not to bail Mr. Putin out of his economic crisis and military mistakes. That effort will face a new test on Friday, when Mr. Biden is scheduled to talk to President Xi Jinping of China for the first time since the invasion, and warn him against supplying weapons to Mr. Putin.

And Mr. Biden’s comments came after three weeks in which the United States and its allies piled sanctions on Russia that the administration insisted were designed to force Mr. Putin to withdraw his forces from Ukraine. But diplomats and intelligence officials from several countries say those sanctions are seen by Mr. Putin as an effort to stoke Russian unrest, turning both wealthy oligarchs and ordinary Russians against his rule.

The White House says that “regime change” in Russia is not on Washington’s strategic agenda. But in past cases when presidents have called national leaders war criminals — Saddam Hussein in Iraq, or Bashar al-Assad of Syria — it has frequently been linked to an effort, covert or overt, to drive them from office.

When promised anonymity, many American officials say that they cannot imagine that Ukraine could be safe from Russian military action while Mr. Putin, stewing in grievances and now angry at his own military’s performance, is still in office.

Last week, William J. Burns, the C.I.A. director and a former U.S. ambassador to Moscow who knew Mr. Putin as he tightened his control over Russia, told the House Intelligence Committee that Mr. Putin’s moves have been “premeditated and savage,” and predicted that “he’s likely to double down and try to grind down the Ukrainian military with no regard for civilian casualties.”

“He has no sustainable political endgame in the face of what is going to continue to be fierce resistance from Ukrainians,” Mr. Burns said.

Other American intelligence officials have said since that Mr. Putin now views this as not only a war to reclaim Ukraine, but to push back on American power — and that he increasingly sees himself wrapped in a struggle with Mr. Biden, whom he views as the last of a generation of Washington Cold Warriors.

Mr. Biden and Mr. Putin have not talked since Feb. 12, almost two weeks before the invasion of Ukraine, when the American president made one last attempt to warn the Russian leader that an attack would lead to crushing sanctions, more arms to the Ukrainians and exactly the result Mr. Putin was trying to forestall: a major buildup of troops and arms on NATO’s eastern front.

Today, it is almost unimaginable that the two men will be dealing with each other directly anytime soon. Hours after Mr. Biden’s “war criminal” comments, the Kremlin spokesman, Dmitri Peskov, called the characterization “unacceptable and unforgivable rhetoric.”

Mr. Putin, for his part, has not said much about Mr. Biden, but he vowed this week to cleanse Russia of “scum and traitors” who he said were being organized by the West as a “fifth column” to destroy the country.

The enmity between the two men has been barely disguised for years, since the day when Mr. Biden, as vice president, by his account told Mr. Putin that he had looked in his eyes and seen no soul. “We understand one another,” Mr. Putin is said to have replied.

But it comes at a moment when Washington’s biggest concern is that Mr. Putin will escalate the war — and reach for weapons of mass destruction.

Just hours before Mr. Biden’s declaration, his national security adviser, Jake Sullivan, told Nikolai P. Patrushev, Mr. Putin’s main national security adviser, that “any possible Russian decision to use chemical or biological weapons in Ukraine” would result in an even harsher Western response. While none would say it publicly, several of Mr. Biden’s aides have been concerned in recent days that if the Russian leader feels cornered — or believes the United States is trying to foment opposition to his rule — the chances that he will reach for such weapons could be heightened.

So the debate underway in Washington now is what, exactly, might trigger Mr. Putin. Some believe he could lash out if dissent in Russia, already visible in street demonstrations, poses a real threat to him. Others believe that his trigger point might be a more direct entry into the war by NATO countries, which are already providing antitank and antiaircraft weapons that have contributed to what the Pentagon now estimates is a Russian death toll of at least 7,000 troops.

One former intelligence official noted that it was Hillary Clinton’s support for street demonstrators who protested the election of pro-Putin lawmakers in Russia that prompted the Russian leader to order the hacks on the Democratic National Committee when Mrs. Clinton was running for president in 2016. Mr. Putin is a believer, the official said, in retribution.

Mr. Putin would have good reason to think the Biden administration is looking forward to his exit, though American officials choose their words carefully to avoid the implication that Washington’s policy is to speed the process. Mr. Blinken, speaking to reporters on Thursday, said that “when all is said and done, an independent Ukraine will be there, and at some point Vladimir Putin will not.”

The last time an American president went head-to-head with a Russian or Soviet leader with so much at stake was 60 years ago, during the Cuban missile crisis, widely regarded as the closest the world came to Armageddon. And yet at that moment, in October 1962, President Kennedy’s instinct was to avoid personalizing the conflict — and to help his Soviet counterpart, Nikita S. Khrushchev, find a way out of direct confrontation.

“I think it is the most natural comparison to this moment,” said Fredrik Logevall, a Harvard historian and Kennedy biographer.

“He kept warning the members of X-COMM,” the committee Kennedy established to guide through the 13 days of the crisis, “that they had to see things from Khrushchev’s perspective,” he said. “He said we had to give him something here to step away. And he was careful in his public comments not to personalize his criticisms of Khrushchev himself. It’s a direct contrast to what Biden did.”

Mr. Putin is not the first foreign adversary Mr. Biden has called a war criminal, as he himself recounted in “Promises to Keep,” a 2007 memoir. He recalled meeting Slobodan Milosevic, the president of Serbia and then of Yugoslavia, who ultimately became the first sitting head of a government to be charged with war crimes.

“He could tell I had just about had it with his lies, and at one point he looked up from the maps and said, without any emotion, ‘What do you think of me?’ ” Mr. Biden wrote.

“ ‘I think you’re a damn war criminal and you should be tried as one,’ ” Mr. Biden wrote. “I was looking right in Milosevic’s eyes, and his expression didn’t change. There was not the slightest twitch in his face. It was like I’d just told him he was a wonderful guy.”

Mr. Blinken said the president was now willing to go further with Mr. Putin, and begin collecting evidence of war crimes. “So when I tell you that there will be accountability and consequences for any war crimes that have been committed,” Mr. Blinken said on Thursday, “I hope you’ll take me at my word, but actions always speak louder than words.”