Fianna Fáil is attempting to recall the Dáil to debate an EU regulation that deals with organ donations.
The move will require the signatures of 56 TDs and must happen before a 27 August deadline.
Sinn Féin has pledged its support for bringing deputies back early from their holidays.
The Seanad will meet to examine a European regulation on organ transplants next Tuesday.
It follows a petition by 20 members of the Upper House, led by Fianna Fáil's Mark Daly, to look again at the issue.
Now Fianna Fáil chief whip Seán Ó Fearghaíl has contacted every TD asking them to get the Dáil to do the same thing.
Sinn Féin said it supports the call because better legislation is required.
Fianna Fáil and Sinn Féin's combined numbers are 33, including Peadar Tóibín, who is currently outside the Sinn Féin parliamentary party.
They hope to get the backing of independents and others to force the recall.
However, advice from the attorney general circulated to all Government TDs today says any recall would be redundant.
The AG says the regulation could only be annulled if an Oireachtas Committee recommended that it happen.