The highly-anticipated summit came at a time when both leaders agree relations between their countries are at an all-time low.
The two met for four to five hours of wide-ranging talks which included discussions on human rights. cyber security and Covid-19.
During a press conference, shortly after the sit-down, Putin was asked whether there was any hostility in his meeting with Biden.
In his response, he said: “As for the over all assessment I believe there’s been no hostility. On the contrary, our meeting took place in a constructive spirit. Indeed we have varied assessments on a number of issues but both sides expressed the intention to understand each other and seek common grounds.
“Talks were quite constructive,” he added.
But Putin said Russia had “provided exhaustive information” to the US in regards to alleged cyber attacks while the US had not responded.
It comes after months of back and forth rhetorics from the pair.
Biden has repeatedly called out Putin for malicious cyberattacks by Russian-based hackers on US interests, a disregard for democracy with the jailing of Russia's foremost opposition leader and interference in American elections.
Ahead of the meeting Putin’s spokesman, Dmitry Peskov, told The Associated Press on Wednesday that no breakthroughs were expected and that “the situation is too difficult in Russian-American relations”.
“However, the fact that the two presidents agreed to meet and finally start to speak openly about the problems is already an achievement,” he added.
When asked whether he had been invited to the White House by Biden, he said no before adding: “I believe that for such meetings and such visits to happen there should be conditions that should be ripe.”
Describing what kind of person he believed Biden is, he said: “I can say that he is a constructive person, well-balanced and experienced seasoned politician and I expected that.
“He recalled his family and conversations he had with his mother. While these things don’t have directly something to do with our business nevertheless it shows his qualities and his moral values - it is all appealing and I believe we spoke the same language.
“But it doesn’t necessarily mean we need to look into the eyes and see the soul and to pledge eternal love,” he added.
Biden opened his conference with a long opening speech about the details of the meeting including what they spoke about and what he requested from Putin.
“I told President Putin my agenda is not against Russia, or anyone else, it’s for the American people,” he said.
The US President said he told the Russian leader that “human rights is always going to be on the table” and “part of the DNA of our country.”
Mr Biden also told Putin that the “bottom line,” was that “we need to have some basic rules of the road that we all need to abide by”.
He described the tone of the meeting as “good” and “positive” and “not done in a hyperbolic atmosphere.”
Arrangements for the meeting were carefully choreographed and vigorously negotiated by both sides.
Biden first floated the meeting in an April phone call in which he informed Putin that he would be expelling several Russian diplomats and imposing sanctions against dozens of people and companies, part of an effort to hold the Kremlin accountable for interference in last year's presidential election and the hacking of federal agencies.
Putin and his entourage arrived first at the summit site: Villa La Grange, a grand lakeside mansion set in Geneva's biggest park. Next came Biden and his team. Putin landed in Geneva on Wednesday shortly before the scheduled start of the meeting; Biden - who was in Europe for a week of meeting with allies - arrived the day before.
After the meeting concludes, Putin is scheduled to hold a solo news conference, with Biden following suit.
The White House opted against a joint news conference, deciding it did not want to appear to elevate Putin at a moment when the president is urging European allies to pressure Putin to cut out myriad provocations.