The party will also face questions after two of its TDs, whose names Mr Adams gave to gardaí, were identified in the Dáil last night during exchanges about the Stack murder.
Dessie Ellis and Martin Ferris strongly denied any connection to the killing.
In an extraordinary turn of events in Leinster House, Mr Adams had sought to address criticism by claiming IRA names must be kept secret for the sake of the peace process.
Mr Stack’s two sons accused Mr Adams of bringing the Dáil into “disrepute”.
“He, in the grossest possible terms, brought Dáil Éireann and the Houses of the Oireachtas into considerable disrepute today,” said Austin Stack.
Austin and his brother Oliver first asked Mr Adams in May 2013 if he could help them secure an IRA confession. Mr Adams arranged a two-hour secret rendezvous with a former IRA leader, to which he brought the two sons in a blacked-out van to the border.
The brothers say the IRA figure knows who shot their father in 1983 and want Mr Adams to give his name to gardaí.
Mr Adams maintains that he provided gardaí investigating the murder with the names of four people earlier this year, which he says were given to him by Austin Stack. Mr Stack denies this.
Amid growing pressure, Mr Adams was forced to make a statement to the Dáil last night.
He said Brian Stack’s killing was wrong and that he had tried to help the family.
He said Austin Stack gave him four names which came from Garda and journalistic sources. Mr Adams gave these to gardaí. Mr Stack denies he gave Mr Adams the names.
Mr Adams said he never described those named as “suspects” but was prepared to co-operate with gardaí.
Separately, he questioned whether giving out names of IRA figures would help the peace process.
Then, in a surprise turn of events, Fine Gael TD Alan Farrell stood up and told the Dáil two of the four names Mr Adams had given to gardaí.
Mr Farrell told the Dáil it was “entirely appropriate” that, given Mr Adams’s statement, that “deputy Ferris and Ellis be given the opportunity to address this house”.
Mr Ellis said he was in Portlaoise jail at the time of the Stack killing and before that, in America. “So you should check your facts, you’re a disgrace,” said the Dublin North West TD.
Mr Ferris, a Kerry TD, said: “I met with gardaí at their request regarding the death of Brian Stack. I co-operated fully with them and I have nothing to answer for.”
Austin and Oliver Stack afterwards claimed Mr Adams had lied to the Dáil. They disputed his version of events. Austin Stack said Mr Adams must give gardaí the name of the IRA figure they met in 2013.
“That individual has information that is pertinent to a live murder investigation,” said Mr Stack.
Labour’s Brendan Howlin said it was “incumbent” on Mr Adams to give this name to gardaí.