Fianna Fáil leader Micheál Martin has said he welcomes the initiation of a process whereby more substantive talks can take place between his party and Fine Gael.
Mr Martin said space and cool heads were required and that people needed to now focus.
He said his party is committed to taking a responsible role in the formation of a government and added that ample time and space needed to be given to those involved in the talks.
Mr Martin said teams of negotiators from both sides would take part and that they would report back to the leaders of both parties.
He said that Fianna Fáil had received a good reception from Independents, but declined to comment on reports that a number of Independents were leaning towards a Fianna Fáil-led minority government.
Yesterday, the two main parties announced that they will meet to discuss how a minority government would work.
Meanwhile, a Fine Gael minister has indicated that a minority government, led by her party, is not a pre-condition for the talks with Fianna Fáil which are due to get under way tomorrow.
Speaking on RTÉ's The Week in Politics, Frances Fitzgerald (below) said a minority government would need very specific agreements in place and would have to examine exactly what a minority government would look like.
Foreign Affairs Minister Charlie Flanagan said a minority government led by Fianna Fáil would not be viable.
He was speaking at an event at the Abbey Theatre to mark the centenary of the Easter Rising and today's 18th anniversary of the Good Friday Agreement.
The Independent TD for Clare, Dr Michael Harty, rejected a newspaper report that the five so-called rural Independents have agreed that they will not support Enda Kenny for Taoiseach.
Speaking on RTÉ's This Week, Deputy Harty said the group has not yet decided who to support for Taoiseach.
Meanwhile, the Minister for Transport Paschal Donohoe said that the talks between his party, Fine Gael, and Fianna Fáil would need to produce a written policy agreement.
Speaking on RTÉ's This Week, Mr Donohoe reiterated that he believed that a three-way coalition offered a viable option. He added that he believed a Fianna Fáil-led minority government would not be stable, but he did not rule out discussing this option.
Also speaking on RTÉ's This Week, Fianna Fáil's Dara O'Brien said he believed that a minority government could work. He said his party remained opposed to a coalition government with Fine Gael and Independent TDs.
