Update 8.49pm: The son of a man killed by the IRA in 1983 has said that his mother was extremely distressed by an offensive tweet.
Sinn Féin Senator Maire Devine retweeted a description of murder victim Brian Stack as a "sadist prison officer".
She was suspended from the party for three months as a result and leader Mary Lou McDonald issued an apology.
Brian Stack's son Austin told Midlands 103 he would like Deputy McDonald to meet his mother.
"I certainly would welcome that, if that was what they were prepared to do, I certainly would welcome that," he said.
"I think my mother would have some very strong words to say to Mary Lou McDonald if that was the case.
"But I will say that the wider issue here is how Sinn Féin conducts its business, and we shouldn't lose track of that.
"The point is here that these are very low standards of public life. This would not be acceptable in any other political party."
Earlier: Taoiseach: Sinn Féin's Máire Devine should face same punishment as Barry McElduff
By Fiachra Ó Cionnaith, in Berlin
Taoiseach Leo Varadkar has called on Sinn Féin senator Máire Devine to resign due to her online comments about murdered Portlaoise prison officer Brian Stack.
Over the weekend, Ms Devine forwarded a message on social media site Twitter which referred to Mr Stack, who was shot dead by the Provisional IRA in the 1980s, as a "sadist".
After initially defending her actions, Ms Devine subsequently said she "deeply regretted" what happened and has been suspended by the party on full pay for the next three months.
Asked about the situation at an event in Berlin today, Taoiseach Leo Varadkar said while the matter is ultimately a decision for Sinn Féin, he believes Ms Devine should face the same punishment as that eventually faced by former Sinn Féin MP Barry McElduff, who resigned over the Kingsmill atrocity references last year.
"I've always taken the view that disciplinary matters are a matter for each individual party, but I have to say I think there's an enormous inconsistency in the way that former MP McElduff in the North was disciplined compared to Senator Devine in the Republic of Ireland.
"It seems that what Senator Devine did was as bad if not even worse. Not only did she disrespect the memory of someone who was a victim of paramilitary violence, she also didn't take it back and continued to engage in it.
"So I see a real inconsistency in that. Somebody in the North has to resign their seat and another person only gets a three-month suspension on full pay.
"So I would call on Sinn Féin to consider that position, to consider whether they should apply the exact same sanction, and also it does appear to be a real concern that despite the change of leadership at the top of Sinn Féin there hasn't really been a change in attitude.
"I think whatever sanction was imposed in the North should be imposed, but obviously that's a decision that party has to make for itself," Mr Varadkar said.