The SNP has said Andy Kerr should not continue as chairman of Labour’s ruling National Executive Committee (NEC) following his anti-Catholic comment.
Mr Kerr was speaking from the stage at Labour’s national conference in Liverpool when he invited a question from a female delegate.
He then appeared to mock her for crossing herself, saying: “Did you cross yourself, there? In that case, I might not.”
Mr Kerr, a deputy general secretary of the Communication Workers Union, later apologised and said the remark was intended to be “light-hearted” but was “ill-judged and wrong”.
Scottish Labour leader Richard Leonard condemned his party colleague’s comment.
Asked if it was “bigoted”, Mr Leonard told BBC Radio Scotland’s Good Morning Scotland programme: “That might be one way of describing it.”
He added: “There is absolutely no room inside the Labour Party for that kind of remark, whether it’s meant as a form of humour or not.
“It’s completely unacceptable and Andy Kerr has unreservedly apologised for the remark that he made.
“There should be no space for it inside the Labour Party and I condemn it.”
Now the SNP has said he should not continue in his current position in the party.
A party spokeswoman said: “Sectarianism is an extremely serious issue and it is important that Labour treats it as such.
“It is untenable for Andy Kerr to continue as chairman of Labour’s NEC - he should go as a matter of urgency.
“Labour are developing a bad habit of trying to brush this kind of behaviour under the rug.”
First Minister Nicola Sturgeon called for cross-party condemnation of Mr Kerr’s comment.
She tweeted: “Andy Kerr’s comment was appalling. The Catholic community is an integral and valued part of Scottish life.
“Everyone who stands for a Scotland where bigotry and sectarianism have no place, and where we positively embrace diversity, must unite to condemn - regardless of party.”