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.
A general election surge in support for Sinn Fein, once the political wing of the Irish Republican Army, upset Ireland's traditional two-party grip on power.
Prime Minister Leo Varadkar's incumbent Fine Gael party, their centre-right rivals Fianna Fail and left-wingers Sinn Fein all received 22 percent of first preference votes, according to the Ipsos MRBI poll issued as the polls closed at 2200 GMT.
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.
A 1998 peace accord that ended three decades of violence over British rule of Northern Ireland in which thousands died requires the two main parties to share power.
A journalist was killed while covering rioting in the border town of Londonderry.
The UN Committee on the Elimination of Discrimination against Women says the UK is violating women's rights by restricting their access to abortion.
British Prime Minister Theresa May and her Irish counterpart Leo Varadkar discuss ways to revive Northern Ireland's Catholic-Protestant power-sharing government which collapsed a year ago.
Sinn Fein has shared power in the British province of Northern Ireland since 2007 and is in talks to restore devolved government there, but it has never governed in the Republic where it has established itself as the third largest party.
"Leadership means knowing when it's time for change and that time is now," Adams told Sinn Fein's party conference in Dublin.
Britain will directly set a budget for Northern Ireland after Irish nationalists Sinn Fein and British unionists DUP fail to agree on a power-sharing executive.
Northern Ireland's main political parties Sinn Fein and DUP have been in talks to form a government since an election in March but are yet to come to an agreement.
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