This morning, David McCaughey, whose cousin Dougald was murdered by the IRA, told BBC's Good Morning Ulster that his family had asked for a public apology from First Minister Nicola Sturgeon.
It follows from the controversial tweet from MSP John Mason last week.
A Scottish Conservative motion has now been laid down condemning the comments.
A spokesman for the Scottish Conservatives said:
"As Mr McCaughey says this morning, John Mason's comments on Twitter were an insult to his family and to the many, many other families who lost a loved-one at the hands of the IRA.
"As Mr McCaughey also says, neither Mr Mason nor Nicola Sturgeon has apologised for these offensive comments. They should do so in order to reaffirm that we all stand against the terrorists who brought so much tragedy and bloodshed to Northern Ireland."