Putin had been asked about Biden's comment during a video call marking the anniversary of Russia's 2014 annexation of Crimea, and he responded along the lines of "it-takes-one-to-know-one", saying his counterpart's words reflected the United States' own problems.
Its embassy in Washington said ambassador Anatoly Antonov was set to depart for Russia on Saturday to discuss "ways to rectify Russia-US ties, which are in crisis".
In an interview broadcast Wednesday, Biden replied "I do" when asked if he thought Putin was a "killer".
In an interview with ABC News, Biden was asked about a USA intelligence report that the Russian leader tried to harm his candidacy in the November 2020 election and promote that of Donald Trump.
But US-Russia relations have deteriorated since then, not only as a result of Russia's annexation of Crimea in 2014 but also against the backdrop of a series of attempted murders blamed on the Kremlin.
Putin's spokesman Dmitry Peskov deplored what he called "very bad remarks by the United States president" that made it clear that "he doesn't want to normalize relations".
In his interview, Biden said he'd had a "long talk" with Putin and had told him, "I know you and you know me".
Putin, within hours, reacted to Biden's ABC interview.
"I know that the USA and its leadership is generally inclined to have certain relations with us, but only on issues that are of interest to the USA and on its conditions", Putin said. Putin's spokesperson Dmitry Peskov said that Biden made clear that "he doesn't want to normalize relations with Russian Federation".
Suggesting Biden was hypocritical in his remarks, Putin said that every state had to contend with "bloody events" and added Biden was accusing the Russian leader of something he was guilty of himself.
White House spokeswoman Jen Psaki was asked by reporters whether the president considers Putin literally or just metaphorically a killer.
In Washington, the State Department noted the Russian move to recall its ambassador and said the USA will "remain clear-eyed about the challenges that Russia poses".
"We are aware of it, we value it and will rely on them in the future", Putin said. "Last time, President Biden initiated a call and now I would like to offer President Biden to continue our discussions".
"I remember in my childhood, when we argued in the courtyard with each other we used to say: it takes one to know one". "That's not a question for us", he said.
"These are really bad remarks by the US president".
In taking a tough stance on Russia, Biden has said the days of the U.S. "On our part, in accordance with our national interests, we will develop relations with all countries of the world, including the United States".
The Foreign Ministry said it expects an explanation from Washington, Interfax reported.
Warning of the risks of "an irreversible deterioration in relations" with the new USA administration, the ministry said Russian Federation still hopes to reverse the downward spiral.