Ian Paisley Junior is under pressure to apologise for homophobic remarks attributed to him in a magazine interview.
The DUP junior minister is alleged to have said that he is 'repulsed' by gays and lesbians and that they harm society.
Sinn Féin and SDLP Assembly members have criticised his comments.
Ian Paisley Junior is currently working with the joint Office of the Assembly First Minister and Deputy First Minister.
In a interview with Hot Press magazine he is quoted as saying 'I am, unsurprisingly, a straight person and I am repulsed by gays and lesbians'.
He also said that 'those people harm themselves and - without caring about it - harm society'.
He further explained 'that doesn't mean to say that I hate them. I hate what they do'.
SDLP spokesperson on Equality Issues, Dolores Kelly, has called on the Assembly to censure Mr Paisley, noting he has responsibility for equality related areas.
Sinn Féin's Martina Anderson said all ministers in the executive had 'a statutory equality duty and should project the rights of everyone, regardless of relgion, sex, race, disability or sexual orientation'.
In 2005, Ian Paisley Jr was formally censured by the NI Policing Board for homophobic comments he made about an adviser to then Ulster Unionist leader, David Trimble.