The six party TDs held a teleconference meeting on Tuesday during which they discussed the coronavirus crisis and government formation.
One source said there was “no dissension” from the position that Labour should go into opposition while another said Mr Kelly expressed a view that was in line with the “thrust” of the general attitude of the meeting.
The results of the contest between Mr Kelly and Mr Ó Ríordáin to succeed Mr Howlin will be announced on Friday. The question of Labour participating in government has arisen because of a view in Fianna Fáil and Fine Gael that they need a third party to form a solid coalition.
Talks between the two Civil War parties continue today but they command only 72 Dáil seats between them, or eight short of majority, and progress in the negotiations has been slow. They have been seeking the support of the Greens, who want a national unity government, and Independents.
It comes as Fianna Fáil leader Micheál Martin faced a call from one of his newly elected TDs to form a national government rather than enter coalition with Fine Gael.
Clare TD Cathal Crowe, who, as mayor of his county, was the first to boycott the State’s commemoration of the RIC earlier this year, made his views known at a meeting of the Fianna Fáil parliamentary party on Tuesday evening.
The meeting also took place via teleconference due to the coronavirus crisis. It was largely taken up with a discussion on coronavirus but Mr Martin gave an update on efforts to form a government with Fine Gael.
John McGuinness, also a Carlow Kilkenny TD, said a government should be formed, and said there was an obligation on Fianna Fáil to talk to all parties since progress with Fine Gael was slow.
Mr Crowe expressed concerns about coalition with Fine Gael and said such a government would not be able to implement policies Fianna Fáil wanted due to the economic damage caused by Covid-19.
He instead called for a national government for the coming months and said coalition with Fine Gael would be damaging for Fianna Fáil.
“He suggested national government for a period while people got to grips with what was going on and it was up to everyone to participate in it,” one TD on the call said.
The Labour leadership election count will be done by video link due to coronavirus. The party has received postal ballots from about 70 per cent of eligible voters to date. It is understood about 2,200 voters were eligible to take part in the ballot.
Those ballots will be sent to Mazars which is continuing to operate as an essential service. Senior counsel Conor Power is expected to count, which starts after midday on Friday, the votes live with video links to the teams of the two contenders.