Biden and Putin's first -- and likely only -- photo op inside their summit was met with a chaotic scene.

According to a pool report, the chaos began outside the room with "10 minutes of a shoving match" between the U.S. and Russian security, press and delegations, with each side aiming to get inside. American reporters were first to go in but not all were let inside.

Already seated, Biden nodded while they shouted questions, including whether the two leaders can trust each other -- but the White House is already disputing that Biden was nodding yes to that.

"It was a chaotic scrum with reporters shouting over each other. @POTUS was very clearly not responding to any one question, but nodding in acknowledgment to the press generally. He said just two days ago in his presser: 'verify, then trust," White House communications director Kate Bedingfield said in a tweet.

Another reporter asked Putin if he feared imprisoned Russian opposition leader Aleksei Navalny and what he would do if Ukraine is allowed to join NATO. Putin didn't answer.

On the way out, another shoving match ensued.

"Lots of shoving and grabbing - it was extremely aggressive," one American pool reporter said. "The Russian security pulled on our clothes and shoved us as we tried to stay in the room. They eventually pushed us out the door."

Inside Villa La Grange, the high-stakes summit has officially kicked off.

Speaking to reporters briefly at the top of their first closed-door sit-down, Putin said he hoped for a "productive" meeting, and Biden said "it is always good to meet face-to-face."

While the scene was chaotic, both leaders looked comfortable. Biden, who was the first to extend his hand for a handshake earlier, sat with his legs crossed, hands in his lap and was seen smiling at several points. Putin also leaned back in his chair, as he often does.

Seated in a library before their respective country's flag and with a globe in between, the pair were joined by U.S. Secretary of State Antony Blinken and Russian Foreign Minister Sergey Lavrov for the first small session of the day.

Following brief remarks from Swiss President Guy Parmelin wishing them well, Biden and Putin shook hands in front of cameras, with both men grinning, before entering the summit site.

Biden and Putin's meeting is expected to last four to five hours total with multiple sessions.

First, they're taking part in a small session, joined by U.S. Secretary of State Antony Blinken and Russian Foreign Minister Sergey Lavrov, ahead of a larger working session.

Biden and Putin are also expected to hold dueling, solo press conferences following the summit.

Swiss President Guy Parmelin wished Biden and Putin "a fruitful meeting" on Wednesday, just minutes before the two leaders sit down for their much-awaited bilateral summit in Geneva.

"On behalf of the Swiss government, I would like to welcome you to Geneva, the city of peace," Parmelin said in prepared remarks in French while welcoming them to Villa La Grange, where the meeting is taking place.

"It is an honor and a pleasure for Switzerland to host you here for this summit and, in accordance with its tradition of good offices, promote dialog and mutual understanding," he added. "I wish you both a fruitful meeting in the interest of your two countries and the world."

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