Social Democrats co-leader Catherine Murphy says Sinn Féin needs to go further to censure Public Accounts Committee (PAC) chair Brian Stanley.
Deputy Stanley is to address the committee over his controversial tweet about two IRA attacks on the British army.
It comes as Sinn Féin confirmed they will not seek his removal as chair of the committee.
Deputy Murphy is also vice-chair of the PAC. She told Newstalk Breakfast his wording will be important.
"I presume that he will explain the tweet, what motivated him: I'll be listening very carefully to what he's apologising for and the impact of the tweet".
She said the tweet "drew quite a bit of attention", and she was taken aback by the message in it.
"I have been on the Commemoration Committee, and we always appreciated just how important it would be to be respectful in commemorating the more difficult era of the War of Independence, and indeed the Civil War.
"And the linkage here, I just couldn't believe that he would have put that tweet out".
'Importance of reconciliation'
She said she "would not have expected this of Brian Stanley, and it was really quite shocking from that perspective".
She said an apology may not be enough.
"I didn't feel that taking it down [and] an apology would be sufficient.
"It has been made clear by Sinn Féin - by Mary Lou McDonald and Eoin Ó Broin - that that is as far as they intend to go.
"I don't find that sufficient, I think there's got to be some degree of censure - but I think that comes down to Sinn Féin".
Deputy Murphy added that while we must remember the past, reconciliation is key.
"Social media is not something that is very easy to control, but I do think that people in positions of responsibility have a responsibility to show leadership.
"We're at a point where we need to appreciate that what is needed, in a post-conflict situation, is an understanding of the importance of reconciliation".
"We have to leave this past behind - that doesn't mean that you don't appreciate what the past is, but I don't think you enflame the situation".