Mr Greenwich has flagged potentially "significant" defamation proceedings, sparked an investigation by NSW Police and lodged a complaint of homosexual vilification and sexual harassment with the Anti-Discrimination Board of NSW.
Despite widespread condemnation, the controversial One Nation MP has refused to apologise for the tweet he posted on March 30 which Mr Greenwich described as "defamatory and homophobic".
The comments were in response to Mr Greenwich calling Mr Latham a "disgusting human being" after LGBTQIA+ protesters were attacked outside a forum where Mr Latham was speaking.
When pressed for an apology, Mr Latham tweeted "never apologise, never explain".
Mr Latham doubled down on the comments during an appearance on TNT Radio last week.
Mr Greenwich said he did not take the action lightly but it was time someone stood up to Mr Latham, saying "enough is enough".
"He made a very sexualised, targeted attack at me on Twitter, seeking to impugn my reputation amongst colleagues, and he has since said that he believes that that's a view that all straight men believe," Mr Greenwich told reporters on Monday.
"He has continued to make comments around whether it is appropriate for me to talk about my sexuality, whether I am in any way possibly considered to be a threat to children.
"Rather than retracting or apologising, Mr Latham continues to reinforce what I consider to be extremely defamatory, vilifying language, directed at me."
Damages could be substantial, Mr Greenwich's lawyer, Nicholas Stewart told reporters.
"After Mr Latham published that tweet, Alex was the subject of ridicule, hatred and contempt," he said.
"This matter is significant - it's actually really serious what Alex has experienced."
Unless Mr Latham apologises, retracts his comments and commits to never make similar statements, defamation proceedings will begin later this week, Mr Greenwich said.
"NSW has really strong homosexual vilification laws ... so we will be pursuing those through the (NSW) Anti-Discrimination Board," Mr Greenwich said.
NSW Police also confirmed an investigation was underway after Mr Greenwich complained of being harassed online.
If Mr Latham is convicted of the offence of using a carriage service to menace, harass or offend, he could be expelled from parliament.
Mr Greenwich's lawyers will also approach Twitter about providing a platform that "freely allows extreme homophobia, transphobia, racism and religious bigotry".
The tweet caused a schism between Mr Latham and One Nation federal leader Pauline Hanson, who said the comments were "disgusting" and called on him to apologise but was ignored.
Premier Chris Minns condemned Mr Latham's comments last month, saying they were terrible and would "unleash ghouls" on the MP.
Mr Greenwich said the premier had been a "great personal support" to him.
Mr Latham was re-elected for an eight-year term at the March election, but the legal action could impact his ability to serve if he is convicted.
AAP has contacted Mr Latham for comment.
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