The Independent Alliance says it will make a decision on Tuesday on whether or not it will back Enda Kenny or Micheál Martin for Taoiseach.
The Dail will vote again on Wednesday, however neither of the men is expected to receive enough votes.
Talks aimed at forming a coalition are due to resume on Monday after taking a break this weekend.
Last night the Taoiseach said he believed they were close to a programme for Government with independents.
However the Independent Alliance's Shane Ross says both Fianna Fáil and Fine Gael need to show a sense of urgency: “There’s no offer on the table at the moment, there’s no final document, there’s no programme for government in draft at this stage.
“What we've done is go through all the topics in enormous detail but we haven’t thrashed out an agreement of any sort. It would be much more helpful if they were to get together and show a real sense of urgency about it,” the Dublin South TD said.
