President Donald Trump has said he wants to find ways to work with President Vladimir Putin, a goal made more difficult by sharp differences over Russia's actions in Syria and Ukraine, and allegations Moscow meddled in the 2016 US presidential election.
The two men met during an informal gathering of G20 leaders at the start of the summit, with the US president reinforcing their handshake by patting the Russian leader on the arm.
In a video of the encounter, President Donald Trump was later shown patting President Vladimir Putin on the back. Both men smiled. They are to hold a formal meeting later in the day at 3:45 p.m. local time, when every facial expression and physical gesture is likely to be analyzed.
"I look forward to all meetings today with world leaders, including my meeting with Vladimir Putin. Much to discuss," President Donald Trump wrote in a tweet on Friday. "I will represent our country well and fight for its interests!"
The meeting is slated to begin shortly after a G20 working session on climate and energy starts. President Donald Trump, who has angered world leaders with his decision to pull the United States out of the Paris accord on climate change, will likely have to leave that session early to make the Russia meeting.
Some fear the Republican president, a political novice whose team is still developing its Russia policy, will be less prepared for their sit-down than Vladimir Putin, who has dealt with the last two US presidents and scores of other world leaders.
"There's nothing ... the Kremlin would like to see more than a (US) president who will settle for a grip and a grin and walk away saying that he had this fabulous meeting with the Kremlin autocrat," Representative Adam Schiff, the top Democrat on the House of Representatives' Intelligence Committee, said in an interview on MSNBC.
As investigations at home continue into whether there was any collusion between President Donald Trump's presidential campaign and Russia, the US president Donald Trump has come under pressure to take a hard line against the Kremlin.
Moscow has denied any interference and President Donald Trump says his campaign did not collude with Russia.
On Thursday, President Donald Trump won praise from at least one Republican hawk in the US Congress after a speech in Warsaw in which he urged Russia to stop its "destabilizing activities" and end its support for Syria and Iran. The remarks were among President Donald Trump's sharpest about Moscow since becoming president, though they stopped short of any personal criticism of Vladimir Putin.
"This is a great start to an important week of American foreign policy," said Republican Senator Lindsey Graham, who has often been critical of President Donald Trump on security issues.
Vladimir Putin had been fully briefed about President Donald Trump's description of Moscow's behaviour as destabilizing, Kremlin spokesman Dmitry Peskov said, adding he would take that and other remarks by US officials into account.
Still, President Donald Trump declined on Thursday to say definitively whether he believed US intelligence officials' assertion that Russia had interfered in the 2016 US election.
"I think it was Russia but I think it was probably other people and/or countries, and I see nothing wrong with that statement. Nobody really knows. Nobody really knows for sure," President Donald Trump told a Warsaw news conference.
Ahead of President Donald Trump's meeting with Vladimir Putin, three US senators wrote to President Donald Trump to express "deep concern" about reports that his administration planned to discuss the return to Russia of diplomatic compounds in Maryland and New York that were seized by the Obama administration last year in response to alleged Russian election meddling.
Republican Senators Johnny Isakson and Marco Rubio and Democratic Senator Jeanne Shaheen said returning the facilities would "embolden" Vladimir Putin and encourage further efforts by Russia to interfere in Western elections. All three are on the Senate Foreign Relations Committee.
The White House declined to offer details on what President Donald Trump would request of Vladimir Putin and what he might offer in exchange for cooperation.
US Secretary of State Rex Tillerson said President Donald Trump wanted to talk about how the two countries can work together to stabilize war-ravaged Syria.
"The United States is prepared to explore the possibility of establishing with Russia joint mechanisms for ensuring stability, including no-fly zones, on-the-ground ceasefire observers, and coordinated delivery of humanitarian assistance," Tillerson said before leaving the United States to join President Donald Trump in Germany.
(Additional reporting by Patricia Zengerle, Susan Heavey and Doina Chiacu in Washington; Denis Pinchuk in Moscow and Denis Dyomkin in Hamburg; Editing by Ralph Boulton)