A group of ten Senators has written to Leo Varadkar seeking a date for the first sitting of the Seanad, without the Taoiseach's 11 nominees, so that legislation can be passed.
The group which includes the former Minister for Justice, Michael McDowell, and Labour's Ivana Bacik, does not accept that the Upper House cannot legally operate until a new government is formed.
The letter, signed by five Labour Party and five Independent Senators, states that the group will apply to the High Court for the judgment, if the Taoiseach does not agree for a date for it to start sitting.
"It is now over two months since the Seanad elections concluded, and longer since the general election, and government talks continue with no clear end point. Our democratic assembly should not be frozen out from legislating," the letter states.
"We intend to apply to the High Court for a speedy, authoritative and binding determination by way of declaration on this important issue of constitutional interpretation unless it is clarified that you share our understanding on this issue and consider yourself constitutionally free to advise the President to fix a day for the first meeting of the newly elected Seanad in early course," the letter tells Mr Varadkar.
While 49 members of the Seanad have already been elected, 11 must be nominated by an incoming Taoiseach. Without agreement on a new government, they cannot be appointed meaning the Upper House is incomplete.
Senator Bacik said the Taoiseach has not publicly stated whether or not it is the view of the Attorney General that the Seanad cannot sit.
"We are asking that the Taoiseach would clarify his understanding of the law. We are asking him in particular to confirm that he can advise the President to convene the Seanad without the need to appoint the 11 nominees. We want the Seanad to sit so that we can go about our business, to be back in the Seanad Chamber and able to legislate," she told RTÉ News.
A crucial point for the House to sit is seen as 30 June. At that point, a motion will need to be passed by both Houses of the Oireachtas to ensure that the non-jury Special Criminal Court can continue to sit.
Those who signed the letter also include: Labour Senators Annie Hoey, Rebecca Moynihan, Marie Sherlock and Mark Wall and Independent Senators Victor Boyhan, Gerard Craughwell, Sharon Keogan and Rónán Mullen.