He said his administration acted in good faith on the evidence available at the time when the decision was taken to release Abdelbaset al-Megrahi on compassionate grounds, saying he had three months to live.
Prime Minister David Cameron's first visit to Washington as premier has been overshadowed by the row over al-Megrahi's release, with US senators suspicious that oil giant BP may have had a hand in the affair.
Mr Salmond was asked on BBC Radio 4's Today programme if he regretted al-Megrahi's release and replied: "No, because you can only take a decision on the basis of the evidence at the time and the decision we took was with due process and in good faith.
"You can only take a decision based on information at the time.
"It's not unheard of for people who have been released on compassionate grounds to live longer than the three months specified."
Libyan al-Megrahi is the only man to have been convicted of the Lockerbie atrocity which killed 270 people in the bombing of Pan Am flight 103 on December 21, 1988.
He was released from a Scottish prison last August but is said to be still alive and living with his family in the Libyan capital Tripoli.
Mr Salmond insisted: "If you take a decision in good faith, you don't regret it."
He criticised ex-premier Tony Blair for negotiating a prisoner transfer agreement (PTA) with Libya in 2007 - which was not invoked for al-Megrahi's release - at the same time as sealing a deal for BP in the country, saying it gave rise to suspicions of "deals in the desert".
He said his administration had consistently opposed the PTA and went on: "As far as the Scottish Government is concerned we had no contact with BP, either written or verbal, as far as the process of compassionate release was concerned.
"The reason they didn't lobby the Scottish Government, I suspect, is because we had made our opposition to the PTA well known and very public."
Mr Salmond added: "We have had absolutely no doubts about the deep feelings and huge, huge hurt about such an atrocity."
But he went on: "Not all the relatives have the same position. Some, though not all, of the British relatives concerned were in favour of the release of Mr Megrahi."
Scottish Justice Secretary Kenny MacAskill said today it would have been a "dereliction of duty" not to take a decision on releasing Megrahi.
And he again stated that he stood by his decision to grant the Libyan compassionate release.
Mr MacAskill told BBC Radio Scotland's Good Morning Scotland programme: "It would have been a dereliction of my duty to have shirked the responsibility that fell to me as the office holder last August.
"I had to deal with it. I couldn't pass it back to the Prison Service, I couldn't pass it to a party of political colleagues, I had to accept responsibility for it."
He added: "I stand by that decision as being the right decision for the right reasons.
"We followed the rules and the regulations and it balanced the beliefs and values that the people of Scotland, I believe, seek to live by, which is that we believe that justice has to be served but mercy must be capable of being shown."
Mr MacAskill said it was undeniable that Megrahi was going to die soon and would have probably done so had he remained in jail.
He said: "Dealing with cancer is not an exact science. If you're far from your home and your family and you're in a prison cell in Scotland, then you can turn your face to the wall.
"If you're at home and you're being treated, then you may live longer. But what is undeniable is that he is terminally ill with prostate cancer, he has been released to Libya and he's going to die very soon."
He added that every application for compassionate release, irrespective of the crime, has been granted by every Justice Secretary in Scotland regardless of their political affiliation.
Former Labour MP Tam Dalyell has written to the United States Senate foreign relations committee, expressing his long-held belief that Megrahi is innocent.
Mr Dalyell, a former father of the House, said he believed Mr Salmond and Mr McAskill also held that view.
He said: "But it would have been impossible for them to say so as senior SNP members because that would have reflected ill on the Scottish Crown Office and the Scottish legal system."
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