Tánaiste Leo Varadkar has claimed Sinn Féin's response to the controversy over social media posts by TD Brian Stanley has been "woefully inadequate".
Mr Varadkar said it "might not be a bad idea and could be helpful" if Sinn Féin leader Mary Lou McDonald made a statement to the Dáil next week, along with her party colleague.
Mr Stanley has already apologised for a tweet said to have been "glorifying violence" by the Provisional IRA in killing 18 members of the British Parachute Regiment at Narrow Water, Co Down, in 1979.
In addition, a 2017 tweet under his name marking Mr Varadkar's election as leader of Fine Gael, read: "Yippee for d tory. You can do what you like in bed, but don't ask 4 a pay rise in d morning."
Mr Stanley has claimed he is not homophobic and has worked to advance gay rights.
However, Mr Varadkar said: "It was something I was going to let pass, to be honest, and I didn't say anything about it until Monday, because I'm not sensitive and I'm not self-righteous and I don't believe in cancel culture.
"And you know, people say things that are homophobic, sexist or misogynistic, but it doesn't necessarily mean that they're homophobic or sexist or misogynistic themselves.
"I think the test really is, how do you respond to what is being pointed out to you? How do you deal with it?"
Mr Varadkar said Ms Mc- Donald in her interview on Today with Claire Byrne on RTÉ Radio 1 on Monday had failed to deal with the issue.
"She tried to explain away what Deputy Stanley wrote, and it's not the first time either," he said.
Mr Varadkar gave the example of another Sinn Féin councillor who he claimed had "made remarks about me that were blatantly homophobic, and racist - and no action was taken by Mary Lou McDonald at the time".
"It was only when it was discovered that he had made misogynistic remarks about women that any action was taken," he said.