During a call yesterday with the Russian President, Mr Biden offered to hold the summit on neutral ground amid growing tensions between Moscow and Washington over border conflicts with Ukraine.
Increasing numbers of Russian troops on the border with Ukraine sparked widespread alarm and warnings from NATO.
But during his call with Mr Putin, the US President reaffirmed Washington’s support for Kiev’s pro-Western government.
He urged Russia to “de-escalate tensions” but also offered to hold his first face-to-face talk with Mr Putin on “the full range of issues facing the US and Russia”.
Konstantin Kosachev, the chairman of the foreign affairs committee of the Russian parliament’s upper house, said the conversation was a “very important step forward”.
He said: “It was a very important step forward… news on a global scale.”
Kremlin spokesman Dmitry Peskov added the offer would be “studied”.
But key figures in Moscow – including Kremlin opponents – have seen the move as a win for Mr Putin.
Garry Kasparov, an outspoken critic of Putin’s regime, said: “A summit?
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Referring to the US readout, Mr Solovyov said: “200 words!
“But where are those on human rights?
“Not a word on gays in Chechnya, not a word on LGBT+ and especially not a single word on Navalny.”
Fyodor Lukyanov, editor-in-chief of the journal Russia in Global Affairs, said the Kremlin would see the prospect of a meeting as a “major achievement”.
He said: “In Russia, the prospect of a meeting will be presented as a major achievement, and in a sense, it is because not long ago Biden said offensive things about Putin and, when asked to talk, said there was no time.”
Mr Biden has been a vocal critic of Mr Putin and last month he was asked whether he thought the Russian president was a killer to which he replied: “I do.”
However, Mr Putin hit back at the remarks and said: “I remember in my childhood, when we argued in the courtyard with each other we used to say: ‘It takes one to know one’.
“And that’s not a coincidence, not just a children’s saying or joke.
“The psychological meaning here is very deep.
“We always see our own traits in other people and think they are like how we really are.
“And as a result, we assess (a person’s) activities and give assessments.”