Mr Robinson was questioned by the BBC on the remarks by his Mid Ulster Councillor, Paul McLean, who wanted homosexuality to be criminalised.
Stewart Dickson MLA said: “These remarks are just the latest in a long line of disgraceful and appalling comments by the DUP about the LGBT community. It beggars belief that Mr Robinson would want men and women to deny their own sexuality. He is completely out of step with British values and core beliefs.
“It is an indication of Mr Robinson’s position on these issues that he did not condemn the views of his Councillor who wanted homosexuality to be criminalised.
“Mr Robinson has got himself tied up in knots. If you are asked a question on this issue then your answer should be that you would not support the criminalisation of homosexuality.
“Members of the LGBT community in Russia have been subjected to horrific intimidation since anti-gay laws were introduced in their country. Would Mr Robinson not be worried about the impact on the LGBT community of homosexuality being criminalised in UK?
“There is a massive campaign to provide posthumous pardons to gay men such as Alan Turing, who helped defeat the Nazis in World War Two, so I would have to question if Mr Robinson would want him to be given a pardon.
“Mr Robinson needs to apologise for these remarks. After Jim Wells’ comments last week, it is clear that we will not see a change in attitude by the DUP towards LGBT issues.”