Moscow has been seeking to expand its influence in Afghanistan following the seizure of power by the Taliban and the exit of most western diplomats from Kabul.
On Wednesday, a Taliban delegation took part in talks in the Russian capital about the future of the country under the so-called Moscow format, which includes India, Iran, China and Pakistan.
During a question and answer session after his speech at the Valdai Discussion Club in the Black Sea resort of Sochi, Putin backed Biden's decision over the controversial U.S. withdrawal.
"Of course, the President of the United States...did the right thing to withdraw his troops from Afghanistan," Putin told the forum on Thursday, according to a transcript on the Kremlin website.
Putin said Biden "probably understood" even if he did not know "in detail" that he would face criticism domestically for the move, but "he went for it, accepted it and took on this responsibility.
"He did the right thing in deciding to withdraw troops but now, of course, we all need to look to the future."
Putin said that "the main responsibility" for the current chaos in Afghanistan was held by "those countries that fought there for 20 years."
"But since they...started this 'mess' they should no longer absolve themselves of responsibility for the events that are taking place and in the future," he said, adding "they have a lot of tools to influence the situation in Afghanistan."
"The first thing they should have done, in my opinion, is to unfreeze Afghan assets and enable Afghanistan to tackle socio-economic problems of paramount importance," he added.