Mr Biden said “nobody believes” he was talking about “taking down Putin”, and claimed his comment was directed at the Russian people.
He added that he was expressing his “personal feelings” during a testy exchange with reporters.
In an emotional speech from Warsaw, made minutes after Russia had fired missiles at Lviv, 40 miles from the Polish border, Mr Biden said: “For God’s sake, this man cannot remain in power”.
The comments widely regarded as the latest in a series of gaffes made in recent weeks, including implying that US troops would enter Ukraine and that the West would respond “in kind” if Russia deployed chemical weapons.
The comment puts Mr Biden’s relations with Western allies under strain and fuelled the Kremlin’s claim that Russia is faced with an “existential” threat.
Speaking on Monday, Mr Biden appeared to blame the media for the White House’s recent clarifications, telling a reporter: “you interpret the language that way”.
Mr Biden denied that his remarks had escalated the conflict, saying it was Mr Putin’s “escalatory efforts” in Ukraine that were “what complicates things”.
Asked why he had added the comment to his prepared remarks, Mr Biden replied: “because I was talking to the Russian people… I was communicating this to not only the Russian people, but the whole world”.
“This is just stating a simple fact that this kind of behaviour is totally unacceptable. Totally unacceptable.”
Pressed again on whether his language would embolden Mr Putin, the US president replied: “I don’t care what he thinks, he’s gonna do what he’s gonna do.
“The idea that he is going to do something outrageous because I called him for what he was and what he’s doing, I think it’s just not rational,” he added.
However Mr Biden said he had not ruled out meeting with Mr Putin again as he seeks to bring an end to Russia’s invasion of Ukraine.
“The question is, is there something to meet on that would justify him being able to end this war,” Mr Biden said.