By appearing before cameras together only for a few moments at the beginning of their meeting, Mr. Biden and Mr. Putin gave little indication of personal chemistry. They shook hands but shared little of the body-language bonhomie that Mr. Trump did with Mr. Putin. In one small area of commonality, Mr. Biden gave a pair of his favorite aviator sunglasses to Mr. Putin, who also loves wearing shades. And Mr. Putin noted that Mr. Biden shared stories about his mother, as he often does.

They each voiced their divergent positions afterward, with Mr. Biden condemning Russian cyberattacks, international aggression and domestic oppression and Mr. Putin engaging in his typical what-about defense by citing objectionable American actions. In a truculent tone, Mr. Putin even defended his crackdown on nonviolent opposition figures like Mr. Navalny by saying he wanted to avoid an insurrection like the Jan. 6 storming of the United States Capitol, a comparison Mr. Biden called “ridiculous.” But they kept their criticisms from becoming personal.

“It was businesslike, it was professional,” said Angela E. Stent, a former national intelligence officer on Russia and author of books about Mr. Putin and the West. “Neither of them really gave ground on anything. But they seemed to have established something that could be a working relationship.”

Fiona Hill, who as Mr. Trump’s senior Russia adviser was so alarmed by his deference to Mr. Putin in Helsinki that she has said she thought about faking a medical emergency to end the session, called this meeting a marked contrast. “It just feels more professional on both sides,” she said.

While Mr. Biden is sunnier and Mr. Putin more dour, they are both seasoned political leaders under no illusions about each other. “Both of them are realists,” she said. “There’s nobody going in there with high expectations.”

Mr. Biden is only the latest in a long line of American presidents forced to figure out how to deal with Mr. Putin, a two-decade story of misjudgment, exasperation and bitterness. A onetime K.G.B. colonel who reversed Russia’s halting post-Soviet experiment with democracy and consolidated power in the hands of a small, well-heeled ruling clique, Mr. Putin has defied all manner of American charm, inducement, pressure and punishment.

President Bill Clinton was the first to interact with Mr. Putin after he became prime minister and considered him “tough enough to hold Russia together,” as he later put it in his memoir, but felt brushed off by the new leader who seemed uninterested in doing business with a departing American president.