Glasgow Shettleston MSP John Mason has been condemned in Northern Ireland for the remarks, made on Twitter, after he was asked to support a campaign to bring the murderers to justice.
The three soldiers - brothers John and Joseph McCaig and Dougald McCaughey, aged 17, 18 and 23 - were serving in Northern Ireland with the Royal Highland Fusiliers.
They were unarmed and in civilian clothes when they were enticed from a Belfast bar to a lonely spot on the outskirts of the city on March 10 1971, where they were shot dead by the IRA.
Their bodies were discovered by children at the White Brae area of Belfast the following day.
The shootings caused widespread disgust and the public mourning led to a political crisis that resulted in the resignation of the then Northern Ireland Prime Minister James Chichester-Clark.
Mr Mason was asked on Twitter to support a campaign to bring the killers to justice, with the message: “Will you support this campaign, or are these brave lads not Scottish enough in your opinion?”
In his response, the SNP MSP said: “Happy to support all campaigns to bring about justice. But not taking sides between Irish and British”.
It was then pointed out that they were Scottish soldiers and was asked if he was refusing to take sides between Scottish soldiers and Irish murderers.
Mr Mason responded: “You say Irish murderers. Others say Irish freedom fighters. I support Scottish soldiers if they do good but not if they do bad.”
The Glasgow Shettleston MSP was also asked if he supported the IRA during the Troubles. His replied that he was not taking sides on Irish issues.
His tweets drew a furious response from Democratic Unionist Party MLA Nelson McCausland.
Mr McCausland said: “This is a grossly offensive remark for which Mr Mason has deliberately not taken the opportunity to apologise for.
“Indeed, when challenged whether his remarks meant he supported IRA terrorism in Northern Ireland he responded: ‘I am not taking sides on Irish issues.’
“Unfortunately we are all too used to republicanism that wallows in the glorification of terrorism. It seems however that some elements of Scottish nationalism also harbour such sentiments.
“It is only a few months since the staff member of another MSP was given an official warning for repeatedly posting messages such as ‘up the Provos’ on social media.
“In 2015 an SNP councillor apologised for quoting the lyrics from a song glorifying the IRA.
“People will rightly ask what exactly the SNP’s position on Irish republican terrorism actually is.
“Will either Mr Mason or his party clarify what he believes three off-duty soldiers in civilian clothes were ‘doing bad’ when they were lured from a city-centre bar to be murdered.
“Will either Mr Mason or his party clarify whether the SNP does ‘take a side’ when it comes to terrorism.
“The members of our Armed Forces who come from Scotland particularly deserve an explanation as to what the governing party in the Scottish Parliament believes about the murder of three Royal Highland Fusiliers in 1971 and the IRA’s murder of so many other service personnel.
“Are the SNP happy to align themselves with a violent terrorist campaign simply because those who engaged in it share their political aim of breaking up the United Kingdom?”
The SNP has been contacted for a response.