Sinn Féin delegates have passed a motion urging the party's leadership to run a candidate in this year's presidential election.
The motion states that "the office of Uachatarán na hÉireann is too important to be uncontested and that the Irish people should not be denied the chance to vote for a Sinn Féin candidate in any election".
It will be now up to the party's Ard Chomhairle to consider the proposal.
Delegates also passed a motion stating that the party leadership should attempt to form a left wing government comprising of parties and independents of a similar political ideology.
Earlier the vice president of Sinn Féin said the time has come for a woman Taoiseach to lead the next Government.
Michelle O'Neill said that woman should be Mary Lou McDonald.
In her opening address to delegates she called for a restoration to power-sharing in Northern Ireland and said Dublin and London should convene the British-Irish intergovernmental conference to remove the obstacles to power-sharing.
She said she and Ms McDonald would meet with Theresa May on Wednesday and would bring that message to her.
Speaking before her party passed a motion calling for a referendum on Irish unity, she said that such a referendum was "coming" and the party needed to be prepared for it.
Sinn Féin's Finance Spokesman Pearse Doherty told delegates that his party was ready and eager to bring passion to the heart of Government.
He said Fine Gael would never understand the anxiety of being one paycheck away from financial distress.
"We hear you when you tell us that you work all the hours you can, you pay your taxes and all of your bills, and at the end of the week you still struggle to make ends meet," he said.
"I hear you, and I say to you, if I am Minister for Finance, I will have your back, Sinn Féin will have your back" he said.
The party's Ard Fheis earlier opened in Belfast with more than 3,000 delegates attending.
The Ard Fheis mark's Ms McDonald's first big test as leader as her party decides its position on the government's abortion legislation.
Two key motions will be voted on: the first will give the party leadership the power to decide policy; the second would allow members to vote according to their conscience.
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The vote will have an impact on whether TDs Peadar Tóibín and Carol Nolan remain with the party.
The party will discuss Brexit, and there will be calls for a referendum on Irish unity, and one motion to be debated calling on RTÉ to boycott the Eurovision Song Contest which takes place in Israel next year.
Ms McDonald will give a live televised address tomorrow night.
.@MaryLouMcDonald and @moneillsf ahead as the #SF18 @rtenews pic.twitter.com/7OhqA05OcS
— Martina Fitzgerald (@MartinaFitzg) June 15, 2018
Additional reporting: Martina Fitzgerald
