Mr Biden was leaving a church service in Washington DC when he was questioned by a reporter about the speech.
When asked if he had been calling for regime change in Russia, Mr Biden replied: “No.”
Senior US officials had spent most of Sunday evening and Monday trying to play down that part of Mr Biden’s speech, which was delivered on Saturday during a visit to Poland.
Among them was Secretary of State Antony Blinken, who said Mr Biden had simply meant that Mr Putin should not be “empowered to wage war” against Ukraine or anywhere else.
• The next round of face-to-face talks between Ukraine and Russia will take place in Turkey starting today
• The Ukrainian region of Luhansk, much of which is controlled by Russian-backed separatists, said it may hold a referendum on joining Russia
• Ukraine said 1,100 people were evacuated from frontline areas on Sunday, including from the city of Mariupol, after both sides agreed to set up two “humanitarian corridors”
• The UN said 1,119 civilians have been killed in Ukraine and 1,790 injured since the Russian invasion began in late February
• Ukraine’s deputy prime minister said Russian forces were “militarising” the exclusion zone around the occupied Chernobyl nuclear power station
Meanwhile, Ukrainian president Volodymyr Zelenskyy said that he is prepared to discuss adopting a neutral status as part of a peace deal with Russia.
Speaking to Russian journalists by video late on Sunday, he said: “Security guarantees and neutrality, non-nuclear status of our state – we are ready to go for it. This is the most important point.”
Mr Zelenskyy, who spoke to the group in Russian, said such a deal would have to be guaranteed by third parties and put to Ukrainians in a referendum.
He ruled out trying to re-capture all Russian-held territory by force, saying this would lead to a third world war.
However, he added that he wanted to reach a “compromise” over the eastern Donbas region, which has been held by Russian-backed forces since 2014.
There would be no movement on other Russian demands, such as demilitarisation, he said.
It comes as another top official warned that Russia is aiming to carve Ukraine in two to create a Moscow-controlled region.
Ukrainian military intelligence chief Kyrylo Budanov said that Mr Putin had realised “he can’t swallow the entire country” and would likely split it like in “the Korean scenario” – a reference to the division between North and South Korea.
Mr Budanov said: “The occupiers will try to pull the occupied territories into a single quasi-state structure and pit it against independent Ukraine”.