Pressure is building on Mark Latham to apologise to Independent MP Alex Greenwich over a homophobic tweet, as the premier accuses the NSW One Nation leader of lowering the level of debate in state politics.

Premier Chris Minns has ruled out working with Mr Latham and his One Nation colleagues Tania Mihailuk and Rod Roberts.

“We won’t go running to Mark Latham and to do deals to get legislation through the upper house,” he said on Tuesday.

“That’s as a result of his repeated coarsening of the politics in NSW.”

The government would not be involved in elevating Mr Latham’s agenda through the parliament and would not give him any senior positions on committees, Mr Minns said.

Mr Latham has refused to apologise after posting a graphic tweet directed at Mr Greenwich last month, leading to widespread condemnation from across the political spectrum.

Mr Greenwich launched a series of legal attacks on Mr Latham on Monday, flagging a potential defamation suit, making a report of online harassment to police and complaining of homosexual vilification and sexual harassment with the Anti-Discrimination Board of NSW.

The deadline for him to respond is Saturday.

Opposition Leader Mark Speakman has refused to rule out working with the controversial MP but says he should apologise.

“They are unworthy comments of any member of parliament,” he said on Tuesday.

“Having said that, the cards I’ve been dealt are the people who have been elected to parliament.

“I have to work with Animal Justice, Legalise Cannabis, One Nation, Labor, the Greens, the Nationals and I will work with anyone who in the parliament.”

AAP has contacted Mr Latham for comment.

By Phoebe Loomes in Sydney