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."

One critical message the president will carry, according to U.S. Secretary of State Antony Blinken, is demanding that Russia stop "harboring in any way criminal organizations engaged in cyberattacks, including ransomware" and urging "Russian cooperation in dealing with these criminal organizations to the extent they're operating from Russian territory."

But tough talk and mounting U.S. sanctions have not deterred Russian behavior, from crackdowns against domestic political opposition and pro-democracy movements to aggression overseas against neighbors Ukraine and Georgia or western democracies and their elections.

Pressed on that Sunday by ABC "This Week" co-anchor Martha Raddatz, Blinken said U.S. sanctions "can be" effective, "especially when they're done in coordination with other countries."

To that end, he emphasized what the administration had said was the importance of Biden meeting American allies in the Group of Seven, NATO and the European Union before sitting down with Putin.

But some of those alliances are bruised after four years of former President Donald Trump's badgering and questioning -- with many Europeans in particular unsure whether "Trumpism" is here to stay or whether "America is back," as Biden has made his tagline for this trip.

Blinken didn't take that political question head on, but he said the U.S. and its allied democracies have "to actually demonstrate in concrete ways that democracies working together are making a difference for their people and for people around the world" -- especially in contrast to Russia and China.

-ABC News' Conor Finnegan