Irish Prime Minister Leo Varadkar resigned on Thursday, but remained an interim leader while the three main parties in the country fight in coalition talks after an inconclusive election.
Mr Varadkar was one of four politicians nominated to be the next Taoiseach of Ireland within the 33rd Dail but failed to receive the majority vote.
At 45 he was well below the 80 needed to take office, but it was a symbolic victory that reflects the rise of the nationalist party in the elections.
Fianna Fail and Sinn Fein each hold 37 seats in the 160-seat Dail, parliament's lower house.
Fine Gael has already said it's intending to go into opposition and not form part of a programme for government.
"If they can not, they should say so and be upfront and honest about their failure, and the empty promises they made", he added.
But its emblematic policy on Irish unity is likely to be an important issue if it gains power. It wants a referendum on sovereignty within five years.
Fine Gael Party suffered a setback: According to the information received, Varadkar's Liberal-Conservative Party Fine Gael Party has suffered a setback.
But Sinn Fein's radical proposals for tackling Ireland's housing crisis and creaking healthcare system proved a powerful draw for young voters in a country that is still dealing with aftershocks of the 2008 global financial crisis, which hammered its debt-driven "Celtic Tiger" economy.
Negotiations may take some time and if they do not come to fruition a new general election may be called.
Mr Martin secured 41 votes in support, with 97 TDs voting against him.
Speaking this afternoon, Green Party Leader Eamon Ryan said that the party had a "positive exchange" with Sinn Féin today and agreed to further talks facilitated by the National Economic and Social Council (NESC) to find "common ground between us and areas where we differ".
'Every party and deputy elected to this house has a right and a duty to represent the mandate they received.
McDonald said Sinn Fein would " talk to everybody because that's what you do in a democratic system, that's what grown-ups do". But both Fine Gael and Fianna Fáil have ruled out a coalition or partnership with Sinn Fein, which was historically the political wing of the IRA. Change means the old order must pass.