While Putin defended Russia on several matters in his news conference, he called the summit with Biden "very efficient, substantive" and offered his fresh impression of the American president to reporters.

"He is very balanced, professional man," Putin said. "He's very experienced. He talked a bit about his family and what his mother told him. They are important things -- maybe they're not quite relevant -- but it does talk about the level of his moral values, which is very attractive," he said.

"And it seems to me that we did speak the same language. Certainly doesn’t imply that we must look into each other’s eyes and find a soul," Putin said, seeming to refer to a past comment from Biden, who says he looked Putin in the eye during a visit to the Kremlin in 2011 and told him he had no soul, a moment Putin said he doesn't remember.

"But essentially, our talks were pragmatic," he said.

ABC News Congressional Correspondent Rachel Scott pressed Putin directly on the fate of imprisoned Russian opposition leader Alexey Navlany.

"The list of your political opponents who are dead, imprisoned, or jailed is long. Alexey Navalny’s organization calls for free and fair elections, an end to corruption. But Russia has outlawed that organization, calling it extremist. And you have now prevented anyone who supports him to run for office," Scott said. "So my question is, Mr. President, what are you so afraid of?"

Putin responded by bringing up the Jan. 6 attack on the U.S. Capitol, and finished by saying, "And fears, I don't want to talk about that. That's absolutely irrelevant."

"You didn't answer my question, sir," Scott said. "If all of your political opponents are dead, in prison or poisoned, doesn't that send a message that you do not want a fair political fight?"

Putin again raised the U.S. insurrection, noting that 400 people were arrested.

"As for who is killing whom and throwing whom in jail, people came to the U.S. Congress with political demands," Putin said. "They face prison sentences of up to 20, maybe even 25 years."

"They are being called 'domestic terrorists.' They are being accused of a number of other crimes," he added, deflecting from Navalny whom he refuses to call by name.

After the summit, Putin was the first of the two leaders to hold a solo press conference.

He said there was "no hostility" between himself and Biden and called their talks "quite constructive" with both sides seeking "common ground," according to a translator.

"I think that both of these sides showed a willingness to understand one another and to find ways to bring our positions closer together," he said through a translator.

Putin said the leaders agreed on the "return of American ambassadors to Moscow and our ambassador to Washington," and regarding cybersecurity, said, "We agreed that we would begin consultations in this respect."

When a reporter asked a question in English about jailed Kremlin critic Alexey Navlany, Putin first laughed, took out his earpiece and claimed he didn't hear what was asked through the translator, before saying he believes Nalvalny "wanted to consciously break the law."

"This man knew he was breaking the laws of Russia. He has been twice convicted," Putin said, refusing to call him by name but instead refer to him as, "the citizen whom you have just mentioned."

The summit between the two presidents ended earlier than expected. Biden was the first to leave -- giving a thumbs-up to reporters as he walked out.

He departed Villa La Grange for his hotel in the "Beast," the armored presidential limousine that had been idling outside.

The two men spent two hours and 38 minutes meeting together, according to the White House -- shorter than up five hours White House officials said their encounter might last.

Next, Putin is expected to hold a news conference. Biden will wait to begin his own press conference until his counterpart's concludes.

When Putin meets Biden on Wednesday in Switzerland, experts in Moscow say for all their differences, the two leaders want something similar from their first summit: to cool things down.

The U.S. and Russia's relations are the worst they have been since the Cold War and since 2016 in particular seem locked in almost permanent crises.

Biden has said he wants a more stable and predictable relationship with Russia, one that would allow it to focus on other foreign policy priorities that are more important to it, like taking a harder line with China. The Kremlin for its part has faced a continuous and intensifying barrage of sanctions-- the latest in April-- and with its crackdown on opposition at home and aggressive actions abroad is increasingly becoming a pariah with western countries.

Since coming to office, Russia has appeared to want to get Biden's attention. The president offered Putin the summit after Russia massed thousands of troops on Ukraine's border in April.

But now, having got Biden to the table, analysts said Putin has a clear proposal to deliver in Geneva: stay out of Russian domestic politics and Russia might act less troublesome abroad.

"The Kremlin wants to transition to a respectful adversarial relationship from a disrespectful one we have today," said Vladimir Frolov, a former diplomat at Russia's embassy in Washington and now a commentator on foreign affairs.

"That is, it wants to be treated the same way the Soviet Politburo was treated by the US in 1970-80s," Frolov told ABC News. "Meaning no name-calling" — such as Biden calling Putin a "killer" — "no personal sanctions on the leadership, no democracy lectures, regular personal summit meetings; respectful tone of discussions, no tangible support for Russian opposition."

It will not be an invitation for détente but instead to return to the later years of the Cold War when Putin was a KGB agent and the Soviet Union and the U.S. saw each other as enemies but tried to maintain a predictable relationship. And, crucially, where Russia was treated as an equal.

"For this, the Kremlin is prepared to promise to behave more responsibly," Frolov said.

"This seems to be in line with what the White House sees as a desirable deliverable," he continued. "So unless one of the leaders stormed out of the meeting shouting expletives, the summit would be a major success."

-ABC News' Patrick Reevell