Former Independent Minister Denis Naughten has said if Fine Gael and Fianna Fail want coalition talks with the regional independents they will have to sit down with controversial TDs Michael Lowry, Noel Grealish and Verona Murphy.
With the Green Party's participation in doubt due to their call for a halt to talks in favour of creating a temporary national crisis government, the regional independent group is set to be a key target of the larger parties' efforts to achieve a Dail majority.
The independents have already held preliminary talks with Fine Gael, Fianna Fail and Sinn Fein. They have urged any two of the larger parties to seek to form a stable majority government.
With Sinn Fein ruled out by Taoiseach Leo Varadkar and Micheal Martin, Mr Naughten conceded that Fine Gael and Fianna Fail were the most likely negotiating partners.
The prospect of a historic Fine Gael-Fianna Fail coalition moved a step closer as they announced they would begin talks as "equal partners" due to the coronavirus crisis.
However, they would still be eight seats short of a Dail majority. The uncertainty over any involvement by the 12 Green Party TDs put the various independent groups in play.
The regional group includes Tipperary TD Mr Lowry - who has been convicted of tax offences - as well as Galway West's Mr Grealish and Wexford TD Verona Murphy, both of whom have been heavily criticised over comments about immigrants.
Mr Naughten insisted they must be included in any upcoming government talks.
He added that the larger parties would "have to talk to Denis Naughten, Sean Canney, Noel Grealish, Michael Lowry, Peter Fitzpatrick, Cathal Berry, Verona Murphy and Matt Shanahan."
He added: "We have spoken to three parties. The ball is in their court now."
Roscommon-Galway TD Mr Naughten is against the Green Party proposal for a temporary national government involving all parties as "significant decisions" with "long-term implications" would have to be taken by ministers over coronavirus and Brexit.
"You need to have ministers that have a clear mandate of Dail Eireann to make long- term decisions," he said.
Fine Gael and Fianna Fail postponed further meetings due to the virus emergency but are expected to renew talks in the coming days.
Fianna Fail leader Mr Martin rejected the idea of a national crisis government, arguing it could lead to "inaction". But one senior TD in the party, Eamon O Cuiv, continued to argue in favour of the proposal last night.