After tight smiles and a firm handshake that made for an image both men wanted the world to see, followed by a chaotic photo op and about three-and-a-half hours of tense talks, U.S. President Joe Biden and Russian President Vladimir Putin emerged to spin their summit at dueling news conferences Wednesday.

Both men called their meeting positive, but while Biden said he raised serious concerns and warned of consequences, he did not claim he got Putin to commit to changing his behavior and the Russian leader accepted no responsibility for cyberattacks on the U.S. or for anything else.

Overall, while Putin gained a fresh presence on the world stage, Biden was under pressure to produce what's being called "deliverables" -- concrete results from how he said he would confront Putin -- and whether he made met his goal of restoring "stability" and "predictability" to the post-Trump superpower relationship, which both Biden and Putin agreed had reached a "low point."

Here are some key takeaways:

As is customary when an American president meets a foreign leader for a major meeting, Biden came bearing gifts.

According to a White House official, the president gave Putin with a crystal sculpture of an American Bison, "a stately interpretation of one of our nation’s most majestic mammals and representative of strength, unity, resilience."

The sculpture was presented on a cherry wood base, symbolic of President George Washington's roots, "with a custom engraved inscription plaque commemorating the meeting," the official said.

And in a touch of Biden's personal fashion, quite literally, he also gave Putin with a pair of custom Aviators made by Randolph USA in the company's Massachusetts factory.

Biden gave a thumbs-up as he boarded Air Force One, leaving his summit with Putin after a week traveling across Europe meeting with world leaders in his first foreign trip as president.

Biden told reporters at the airport he thinks he succeeded in what he said was his main mission of showing, on the world stage and to G-7 and NATO allies, that "America is back."

"They're glad America’s back -- and they acted that way," Biden said, offering final thoughts on his high-profile trip.

Biden reiterated that world leaders “thank[ed] him for arranging a meeting with Putin, and said he was a better position to represent the West "knowing that the rest of the West was behind us," adding he owed them all a "debt of gratitude."

When asked on his way out of his solo press conference by CNN's Kaitlin Collins why he was confident Putin will change his behavior, Biden walked back toward reporters, raised his finger and said, "What the hell?... When did I say I was confident?"

Collins followed up noting Biden said earlier it would take "six months to a year" to see if the U.S. and Russia "have a strategic dialogue that matters."

"What I said was, let’s get it straight. I said what will change their behavior is if the rest of the world reacts to them and it diminishes their standing in the world. I'm not confident of anything. I'm just stating a fact," he said.

When she followed up again, Biden said, "If you don’t understand that, you’re in the wrong business."

But by the time he arrived at Air Force One a short while later to return to Washington, Biden walked over to reporters and apologized.

"I owe my last question an apology. I shouldn’t have -- I shouldn’t have been such a wise guy with the last answer I gave," he said. "Anyway. Thanks for being here," adding he feels good about where the country is headed following his first foreign trip.

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