The former Liberal Democrat leader called on Mr Salmond to apologise for saying he admired "certain aspects" of Mr Putin's leadership in a magazine interview.
The peer - who was the international High Representative for Bosnia and Herzogovina - said the First Minister had failed to learn from his controversial opposition to Nato intervention in the conflict in the former Yugoslavia.
Mr Ashdown said: "The events leading up to Kosovo showed that Salmond was, in the words of the late Robin Cook, "unfit to lead".
"Once again, he is on the wrong side of human rights groups and civil society.
"He needs to show he has learned from his mistakes and apologise for these remarks."
Lord Ashdown said Mr Salmond's comments were out of step with other Western governments. He added: "I know when he says this he does not speak for Scots.
"But governments around the world attempting to establish independent Scotland's approach to foreign policy will have heard his praise for Putin loud and clear." In the interview the First Minister stressed he did not agree with all aspects of Mr Putin's leadership but praised him for restoring Russian pride.