Update 5.21pm: Fianna Fáil has described today's meeting with Fine Gael as "constructive".
"Contacts between both parties will continue over the weekend and it was agreed that they will both meet again on Monday," the brief statement concluded.
Earlier: Talks between Fine Gael and Fianna Fáil on forming a minority government led by Enda Kenny have finished for the day,writes Juno McEnroe, Political Correspondent.
Informed sources described the two-hour talks as having "gone well" and that they would resume on Monday.
It is now thought that Fine Gael will also target Independents in a parallel process as it bids to build the foundations for a deal on setting up a minority government.
The two teams from the big parties met at Government Buildings today after getting the imprimatur from their leaders earlier in the day to resume negotiations.
It is thought that the two teams will now break off contact for the weekend.
However, it remains unclear whether any negotiations will produce a result by next Wednesday, when the Dáil is due to return, for a fourth attempt at electing a Taoiseach.
Party sources today played down that scenario and pointed to the fact that there were still many issues to iron out, which could take up to two weeks.
Earlier Mr Kenny made contact with Fianna Fail leader Micheál Martin by phone.
A “cordial” and “professional” conversation was held between the two this morning after the Fianna Fáil parliamentary party formally last night agreed to back the minority government.
A number of stumbling blocks have yet to be overcome, however, before Mr Kenny can make history by becoming the second Fine Gael Taoiseach consecutively returned.
These include an agreement on how long the Government would last, the numbers of Independents who will back Mr Kenny’s administration and ironing out major policy differences between his party and Fianna Fáil, including on the future of Irish Water.