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.
Global chaos continues as deaths rise in Iran and Italy owing to deadly virus first detected three months ago in China.
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.
"We'll want to cooperate and we expect the EU to follow through on their commitment to a Canada-style free trade agreement," says British Foreign Minister Dominic Raab.
The main sticking point in the Brexit deal is how to keep open the border between the British province of Northern Ireland and the Irish Republic, a member of the EU.
UK PM Johnson's offer focuses on a complicated proposal for preserving a free-flowing border between British-run Northern Ireland and EU member state Ireland after Brexit.
The nominations came after one of the longest summits in recent years, outstripping even all-night negotiations during the Greek debt crisis.
Theresa May's announcement to resign as British prime minister on June 7 sparks a flurry of reactions.
European leaders offered Britain a six-month delay to its Brexit departure, officials said. Britain's PM Theresa May, who had sought a delay only until June 30, has agreed to the offer.
In the two years since Article 50 was triggered, the long, arduous process that is Brexit has been whittled down to one complicated term: the backstop. What is it and why is it holding things up?
EU leaders have rebuffed May's request to sweeten the divorce agreement and help her win over a hostile UK Parliament, and Juncker complained to reporters about a political climate which was sometimes "nebulous, imprecise."
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