Connolly, from Galway, who has been a TD since 2016, was backed by the major left-wing parties – Sinn Féin, Labour, the Social Democrats, People Before Profit, and the Greens.
Speaking to BBC NI’s Sunday Politics programme, Sinn Féin president Mary Lou McDonald said the result of the presidential election had boosted her confidence of leading a left-wing coalition into government in the Republic of Ireland after the next general election.
“I think we need to work in common cause, in a collaborative way, to find means and mechanisms to repeat this moment of hope,” she added.
“This moment of real evidence of success and achievement and a win for politics beyond Fianna Fáil and Fine Gael.”
During the election campaign, Connolly sought to establish herself as a united Ireland candidate and said she would like to see a border poll on the island of Ireland during her presidency, which runs for seven years.
McDonald said she expected to see a border poll during Connolly’s presidency and was “so happy” that Ireland had a president who “appreciates and recognises that the preparations for those referendums needs to happen now”.
“I believe that Catherine’s presidency is the time where we will see the calling of the referendums, I have said for many, many reasons, the extent of change, political change, demographic change, all across Ireland,” she said.