It's the longest time on record it's taken to form a government in the country
Fine Gael and Fianna Fáil will maintain contact this weekend following constructive talks on Friday.
Official negotiations, aimed at forming a Fine Gael led minority Government, will resume on Monday.
Friday's talks, which came off the back of a phone call between Enda Kenny and Micheál Martin which was described as coriald and professional, were believed to be brief.
Fine Gael still needs the backing of another six independents, in addition to the two who are already on board.
Meanwhile, former Tánaiste Micheal McDowell says he believes that Fianna Fáil will be very happy to be in opposition.
Mr McDowell says they see Enda Kenny as a liability as Taoiseach.