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.

Amid all the high-level shadow boxing setting up President Joe Biden's summit with Russian President Vladimir Putin, Biden has added a new wrinkle -- one that amounts to a test for himself that awaits him back home.

Biden has cast this moment in the world community in broad terms for the United States -- a chance to assert the power of democratic nations in the face of challenges from China and Russia in particular. Asked Monday what he is telling allies who may be worried about any American slide toward autocracy, Biden again went big.

"What I'm saying to them is, watch me," Biden said. "That's why it's so important that I succeed in my agenda."

Biden was nonchalant in his condemnation of what he called the "phony populism" of former President Donald Trump. Speaking about Republicans, he flatly observed that "the Trump wing of the party is the bulk of the party, but it makes up a significant minority of the American people."

Still, just hours earlier, Senate Minority Leader Mitch McConnell served notice that his brand of hardball is still going to be played, with a warning about what Republican Senate control would mean for any Supreme Court vacancy under a Democratic presidency.

McConnell is objecting to congressional scrutiny of Trump-era Justice Department strategies, just like he did to the proposed Jan. 6 commission. And it's still far from clear whether any infrastructure or climate-change legislation can pass with Republican support, to say nothing of the prospects for tax reform.

Asked about Putin's laughing response to Biden's assertion that he is a killer, Biden said his message back would be that he is laughing as well. The world now is watching -- and will still be when Biden and Putin are both back home.

-ABC News Political Director Rick Klein