Russian President Vladimir Putin thanked US President Joe Biden for the initiative of their summit.
Opening the summit, Putin said he hoped for a "productive" meeting.
"I know that you had a long trip and lots of work. Nevertheless, we have lots of questions stocked in Russia-US relations that require discussion on a high level. I hope our meeting will be productive," Putin said.
Putin and Biden were meeting on June 16 at the lush lakeside Swiss mansion for their highly anticipated summit.
The two leaders shook hands while appearing briefly before cameras with Swiss President Guy Parmelin, who welcomed them to Switzerland, and then entered the mansion for what is expected to be four or five hours of talks.