Ms Hanson, who appeared at an anti-transgender rally last week in Canberra, took to Twitter on Thursday to condemn Mr Latham's homophobic attack.
"I want you to know I don't condone them (Mr Latham's words) and neither do my members of parliament or party associates," she said.
"I think they are disgusting".
Mr Latham joined Pauline Hanson's One Nation party in 2018. He was voted in again in his upper house seat in the NSW election on Saturday.
She said she tried ringing the firebrand MP "a couple of times to no avail" asking him to issue a public apology.
"It is now over to Mark to answer the people".
Mr Latham's tweet was posted in response to an article in which Sydney independent MP Alex Greenwich called the NSW One Nation leader "a disgusting human being" after LGBTQI protesters were targeted outside an event Mr Latham was speaking at.
"Disgusting?" Mr Latham said, before disparagingly describing sexual acts in a mocking tone.
The tweet, posted on Thursday morning, was deleted within a few hours but not before several Twitter users took screenshots and reposted the comment.
Mr Greenwich told AAP he would not be commenting on the matter, but later tweeted: "For those wondering how I'm doing after Latham's homophobic attacks today, I'm fine and I'm more motivated than ever to deliver long overdue LGBTIQA+ reforms.
"... and I have the most handsome husband," he posted, along with a photo of him and his partner Victor Hoeld.
NSW Labor upper house leader Penny Sharpe said she was "physically sickened" by the now-deleted tweet, in which Mr Latham made comments about Mr Greenwich's sexuality.
"Homophobia is always unacceptable and there is never an excuse," she said.
"Mr Latham should apologise to Alex Greenwich immediately."
AAP has contacted Mr Latham for comment.
Mr Greenwich earlier criticised Mr Latham after a mob of hundreds of people attacked LGBTQI activists outside a church in southwest Sydney in the lead-up to the NSW election.
The small group of peaceful protesters were surrounded and threatened by 'Christian Lives Matter' activists outside the event in Belfield, where Mr Latham had been invited to speak about parental rights.
Three men were charged following the incident.
"No one should take the law into their own hands. Violence at political events is wrong," Mr Latham tweeted at the time.
16°C