A series of independent TDs have indicated that they will not support any candidates in this week's vote to appoint a Taoiseach.
Both the Independent Alliance and the so-called Rural Alliance are likely to abstain in the vote on Wednesday.
Many independents have criticised the failure of the two large parties to begin any talks over the weekend.
Michael Healy-Rae said that the parties are acting as if they want Independents to run the country.
"The party leaders want us to make up our minds on Wednesday," he said.
"And they want us to vote before they'll really sit down and talk to each other.
"I mean, do they want the independents to run the country for them altogether so, because, I mean, standing back, they're sort of saying: 'Well, we won't talk to each other until we see what the independents will do.'
Update 4.32pm: Sinn Féin TD Martin Kenny has said that Enda Kenny and Micheál Martin both need to realise that neither can govern without the other.
“Micheál Martin’s refusal to talk to Enda Kenny before this week’s nominations for Taoiseach shows that they are not serious about sorting this issue and are still jockeying for position,” he said.
“Does Micheál Martin realistically believe that he can be elected Taoiseach this week?
“Similarly, Leo Varadkar’s tweet last night shows that they are just going through the motions and not dealing with this situation with any urgency or seriousness.
“They have an eye on the next election rather than the formation of a government that will deal with the issues facing the people.”