Meanwhile groups of Independents are also due to meet to decide on their next move.
After meeting for 90 minutes last night the same short statement was issued by both parties saying the talks were constructive and cordial.
It's understood the four negotiators from each side did not get into great policy discussion, and that the meeting was more about building trust.
They'll resume discussions today.
Meanwhile groups of Independents are also expected to meet today to decide how they should proceed – but it appears there are splits in their ranks about whether they would support a Fine Gael led or Fianna Fáil led minority government.
