Sinn Féin leader, Mary Lou McDonald, has written to Fianna Fáil leader, Micheál Martin, to set up a meeting following General Election 2020.
Ms. McDonald has already met with a number of the smaller parties to discuss government formation.
It comes as Fianna Fáil's parliamentary party meets for the first time today, since it lost eight seats in the general election.
Fianna Fáil is split on what to do next and whether or not to work with Sinn Féin.
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