A group representing the Ukrainian diaspora in Scotland said that the First Minister should issue a "sincere apology" for his controversial remarks praising the Russian President.
Mr Salmond has come under fire after comments that he admired "certain aspects" of Mr Putin's leadership.
Michael Ostapko, chairman of the Scottish branch of the Association of Ukrainians in Great Britain, Scotland, said: "I have been overwhelmed by the reaction of the Ukrainians in Scotland to the comments.
"They are variously insulted, dismayed and upset that a high-profile politician aspiring to some favoured position in the history of these freedom loving isles should make poorly considered, erroneous and mistaken assessments and to express admiration of a dictatorial and criminal regime."
The Russian leader faces intense international criticism over his actions in Ukraine, as well as accusations of corruption, war crimes, human rights abuses, repression and of protecting President Assad's murderous regime in Syria.
Mr Ostapko attacked "lame excuses" about the date of the interview, which was March 14 as Russian troops were amassing on the Ukrainian border.
"The facts are that occupation of the Crimean parliament took place at the end of February," he said, "followed by the unconstitutional illegal 'referendum' on 16 March, organised by a government which had been taken over at gunpoint by a party that gained only 4% of the vote in the 2012 election, and supported by Russian soldiers and gangs of men equipped and armed by Russia.
"Mr Salmond's words can only give succour to the perpetrator of such undemocratic action."
Former Labour Europe minister Jim Murphy also called on Mr Salmond to apologise.
In an interview with Alastair Campbell, Tony Blair's former spin doctor, for GQ magazine, the First Minister said he admired "certain aspects" of Mr Putin's leadership.
Asked about the president, Mr Salmond said: "I don't approve of a range of Russian actions, but I think Putin's more effective than the press he gets, I would have thought; and you can see why he carries support in Russia."
Pressed on whether he admires the Russian leader, he said: "Certain aspects. He's restored a substantial part of Russian pride and that must be a good thing."
The Scottish Government said: "The First Minister will reply directly to this letter making clear, as he did in the GQ interview, that he disapproves 'of a range of Russian actions'. The Scottish Government is entirely opposed to the Russian Government's stance on human rights, homosexuality and the illegal annexation of Crimea.
"Since this interview was conducted the Scottish Government has made our position abundantly clear on the illegal annexation, including the decision to withdraw the invitation to the Russian Consul General to the annual Scottish Consular Corps dinner.
"The Scottish Government has a firm and enduring belief there is no place for prejudice or discrimination - in Scotland or any other part of the world - and we strongly condemn human rights abuses wherever they take place."