The took place at a Las Vegas hotel on Wednesday where fans of the Glasgow club have gathered for the annual North American Federation of Celtic Supporters Clubs conference.
Compston, who is a club ambassador with Celtic, is filmed on stage with others in front of the jubilant fans as a version of ‘Beautiful Sunday’ by Daniel Boone is sung with IRA chants added.
The actor Compston later issued a statement on Twitter saying he “did not sing ANY sectarian songs”.
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He said: “Let me be absolutely clear, I unequivocally did not sing ANY sectarian songs. I’ve worked in Belfast too long to see damage done to think this stuff is a laugh.”
He goes on to say: “If it was an IRA song and I was on stage bobbing along I would understand the story, but I’m pretty sure Daniel Boone had nothing more than Beautiful Sundays in mind when he wrote the song and that’s what I was singing.”
However, Compston’s statement has been branded “utterly inadequate” by DUP leader Sir Jeffrey Donaldson.
Sir Jeffrey tweeted: “I like @martin_compston as an actor but his statement is utterly inadequate. The PIRA was responsible for 1,705 murders. 48% of Troubles deaths, including Scots.
“He should condemn those chanting about PIRA and do more to dissuade such behaviour in future.”
Former senior police officer Jim Gamble tweeted: “He has issued a statement saying he didn’t sing the words attributed to him. I think you have to take his word for that unless there is proof he did. IMO it was an error for him to put himself in a position that created such a negative impression.”
Another former PSNI officer, Jon Burrows, tweeted: “This wont cut it. Martin needs to make clear he condemns such glorification of murder, torture & extortion. The video speaks for itself & this is not a credible response. Men with far less influence & resources paid a heavy price (quite rightly) for such behaviour recently in NI.”
The Nil by Mouth campaign group in Scotland said: “This is a pretty depressing spectacle and those involved in the IRA chanting need to take a long hard look at themselves in the mirror. These are adults not children who might not know any better.
“The worst thing? Children and young people could see this and now think this is totally acceptable behaviour.”
Mr Compston’s agent was asked to clarify if the actor condemned the IRA and condemned the singing of pro-IRA songs.
The Hamilton Hodell agency said: “Martin’s statement regarding this is on his Twitter.”
The BBC was also contacted, but said, “we won’t be commenting on this”.