"Mark Latham and his behaviour over the last couple of days is completely unacceptable," Penny Sharpe told reporters on Saturday.
"There's no place for it in NSW. There's no place for it in NSW politics. There's no place for it in our community."
Late on Friday, One Nation MP Mark Latham tweeted "Never apologise, never explain" in response to his own homophobic tweet that sparked widespread condemnation and led NSW Premier Chris Minns to label him a "bigot".
The post came after more than a day of silence from Mr Latham, since he posted on Thursday in response to a news article about a violent protest outside a church he spoke at during the state election campaign.
In the article, independent MP Alex Greenwich branded Mr Latham a "disgusting human being" who posed a risk to the state.
"Disgusting?" Mr Latham wrote before making a graphic and homophobic description of sex acts.
The parliament is currently unable to discipline Mr Latham, Ms Sharpe said, as he used a loophole in the upper house system allowing him to resign as an MP before the state election and recontest his seat.
Mr Latham is set to return to parliament during the next session, with a renewed eight year term.
"The best thing that Mr Latham could do is to apologise to Mr Greenwich," Ms Sharpe said.
"That's what we want him to do today.
"Let's see in terms of what happens after the press of the button on the upper house ballot on the 20th of April."
Mr Latham has deleted his original tweet, but its content invited broad criticism, including from the federal leader of One Nation, Pauline Hanson, and conservative commentators Ray Hadley and Andrew Bolt.
"I think that they're vile and shameful comments and I think (Mr Latham) revealed himself to be a bigot," the premier said at the Lifeline International President's Lunch in Sydney on Friday.
Mr Greenwich was an "extraordinarily effective" politician who "manages to elevate the conversation and make major changes in the state," Mr Minns said.
"One of the things that can't be forgotten is that comments like this, even though in and of themselves they're terrible, they unleash ghouls on people like Alex.
"It's not what we need in public life.
"There should be an unambiguous and universal condemnation of these comments," he said.
The tweet was also called disgusting by Transport Minister Jo Haylen, who said she did not think the NSW One Nation leader was up to his job.
"Of course he should apologise but it's Mark Latham. I don't think anyone should be holding their breath.
"Personally I don't think he is fit for public office."
The homophobic attack briefly brought Mr Greenwich to tears on Thursday, the popular Sydney MP told reporters.
"This has obviously been hurtful for me. I had a bit of a cry late yesterday at the end of the day," he told reporters on Friday.
"After being in this gig for a decade and getting re-elected, I didn't think I'd still be subjected to homophobic abuse."
However, Mr Greenwich refused to call for Mr Latham to apologise or resign.
"I don't want to give him another soapbox for him to pretend to be a victim when he seeks to victimise people."
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