Mary Lou McDonald's attempts to "play down" Brian Stanley's tweets "sends the wrong message", Leo Varadkar has said.
The Sinn Féin TD, who is chair of the Public Accounts Committee, will come before the Dáil next Tuesday to address the controversy over a number of social media posts, one of which was taken as being homophobic towards the Tánaiste.
Mr Stanley tweeted in 2017: "Yippee 4 d tory. It's Leo. U can do what u like in bed but don't look 4 a pay rise the next morning."
Mr Stanley says the meaning of the tweet has been "twisted".
However, Mr Varadkar says he "looks forward to hearing his explanation".
"He is coming before the Dáil next week - I think that's good. I think he should answer questions.
"I know that's not the precedent when it comes to the opposition, but we've changed the rules in the Dáil many times.
"When the opposition demands accountability I think they should agree to take questions on this too."
Mr Varadkar says he may have been made aware of the tweet at the time, but only spoke out yesterday.
"I wasn't gonna say anything about this," he said.
"I said nothing about it until yesterday, because I understand the world we live in. People can say things from time to time, that are homophobic or racist or misogynistic. It doesn't mean that they in themselves, are necessarily homophobic, or racist or misogynistic.
"What does matter is how they respond to it, and if it's pointed out to them; how do they engage?
"And that's why I was very disappointed by the response (from Mary Lou McDonald)... This isn't the first time it has happened, by the way, you know one of the councillors during the election made blatant remarks about me that we're both racist and homophobic, nothing was done.
"It was only when he turned out to make remarks about young women that something was done.
"I think the fact that Mary Lou McDonald, kind of tried to explain all this stuff away, play it down, sends out the wrong message.
"There is a culture in Sinn Féin of bullying and intimidation, 20/30 of their councillors have resigned in the past five or six years.
"I think, in the way they're dealing with this, they do send out a message that if you're a Sinn Fein supporter, and, you're gay or you're young woman, or you're mixed race, you'll be celebrated, but if you're an opponent of Sinn Féin, and you're gay, or you're mixed race, or you're a young woman, that's fair game. You see that in the way they conduct themselves. I have a problem with that."