Vladimir Putin childishly responded "it takes one to know one" after Joe Biden described him as a "killer".
The Russian President challenged his US counterpart to a televised discussion to be broadcast live.
Putin scathingly responded to Biden's remarks with the comment that it takes one to know one.
It comes after an ABC News in which Biden said "I do" when asked if he believed Putin was a killer.
It prompted Russia to recall its Washington ambassador for consultations.
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.
"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," Putin said.
"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," he said.
Putin proposed they had another conversation, on Friday or Monday, to be held by video-link and broadcast live.
"I want to offer President Biden to continue our discussion but on the condition that we do it live, online, without any delays but in an open, direct discussion," Putin said, asked in a television interview about Biden's comments.
The two leaders last spoke by telephone on January 26, soon after Biden took office.
In his comments, Biden also described Putin as having no soul, and said he would pay a price for alleged Russian meddling in the November 2020 US presidential election - which the Kremlin denies.
Russia is preparing to be hit by a new round of U.S. sanctions in the coming days over that alleged meddling as well as over an alleged hack.
