Pressure is mounting on who Independent TDs will support in the formation of a new government.
Fianna Fail leader Micheál Martin says he will talk to Enda Kenny again next week - after the Dáil makes another attempt to elect a Taoiseach.
The two men spoke on the phone yesterday for around 20 minutes.
Fresh talks next week is seen as major progress towards forming a new coalition, as Fine Gael holds ongoing talks with the group of 15 Independents.