Taoiseach Micheál Martin has said Sinn Féin TD Brian Stanley should apologise for his comments in relation to the 1979 Warrenpoint bombing and the British establishment.
Mr Martin said the chair of the Public Accounts Committee also needs to apologise and account for his tweets in relation to Tánaiste Leo Varadkar.
Speaking on RTÉ's Morning Ireland, Mr Martin said he would like to see what Mr Stanley will say tomorrow when he addresses the Dáil and to give him the opportunity to make a comprehensive statement and apology.
Sinn Féin leader Mary Lou McDonald said Mr Stanley will not be resigning but will set out his stall and make his position clear when he makes a statement to the Dáil.
Ms McDonald said there can be good use of social media but it can also be misused or "sloppily used".
Laois Offaly TD Mr Stanley has since deleted his twitter account following the controversy.
The Minister for Higher Education has said Mr Stanley should make a statement, apologise and take questions tomorrow.
Simon Harris said Sinn Féin need to hold themselves to the same standard as they hold Fine Gael.
He said it was open to Mr Stanley and party colleague Martin Browne to take questions if they wish.
Meanwhile, the Irish-Syria Solidarity Group has expressed concern about tweets by Sinn Féin's foreign affairs spokesperson John Brady on Syria.
The ISSG says that Deputy Brady, along with other party members, questioned whether President Bashar Al-Assad had used chemical weapons against his own people.
The Organisation for the Prohibition of Chemical Weapons has previously found that the Syrian Army did use chemical weapons in aerial attacks.
The group has called on Sinn Féin to clarify its position.