Martin's election follows months of negotiations between his centre right party, Fine Gael, and the Green Party, to reach an agreement following elections in February before the onset of the coronavirus crisis.
Talks among the parties have failed to make much progress since the February 8 election, which brought a breakthrough for left-wing nationalists Sinn Fein at the expense of the two long-dominant centrist parties, Fianna Fail and Fine Gael.
The three-way race led by left-wing Sinn Fein is a new dynamic for the Republic, where governments have been historically dominated by Fine Gael and Fianna Fail.
Ireland's Deputy PM Frances Fitzgerald said in a statement that she stepped down for the sake of the country, averting a snap general election.
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