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.

Biden said he raised with Putin -- and will continue to raise -- cases like jailed opposition leader Alexei Navalny, the two "wrongfully" imprisoned Marine veterans, Paul Whlean and Trevor Reed, and the ability of Radio Free Europe and Radio Liberty to operate, for starters.

However, he did not claim he caused Putin to change his behavior on those matters, signaling he thought the face-to-face meeting in itself a success.

"There were no threats, just simple assertions made. And no, 'Well, if you do that then we'll do this' with anything I said. It was just letting him know where I stood, what I thought we could accomplish together, and what, in fact, if there were violations of American sovereignty, what would we do," Biden said of the meeting.

On cyberattacks, Biden said they agreed to task expert in both countries "to work on specific understandings about what's off-limits and to follow-up on specific cases that originate in other countries." Putin refuses to say Russian hackers are to blame for some of the recent cyberattacks, despite U.S. intelligence indicating otherwise.

On the Middle East, Biden said Putin raised the withdrawal of U.S. troops in Afghanistan. He also said they agreed it's in the interests of both nations not to let Iran acquire nuclear weapons.