If Sinn Finn emerges victorious, it will be entitled to the post of first minister in Belfast for the first time since Northern Ireland was founded as a Protestant-majority state in 1921.
But the party has kept such issues low down on its agenda during a campaign that has been dominated by more immediate concerns, namely the skyrocketing cost of living.
With about 50 of 90 seats counted so far, results showed that Sinn Fein has 18 seats, while the Democratic Unionist Party, which has been the largest in the Northern Ireland Assembly for two decades, have 13.
The centrist Alliance Party, which doesn’t identify as either nationalist or unionist, has seen support surge and has 10 seats so far.
A unionist party has held the role of Northern Ireland’s first minister since the 1998 peace agreement that ended decades of Catholic-Protestant conflict. Under a power-sharing system created by that agreement, the jobs of first minister and deputy first minister are split between the biggest unionist party and the largest nationalist one.
Both posts must be filled for a government to function, but the Democratic Unionist Party has suggested it might not serve under a Sinn Fein first minister.
The DUP has also said it will refuse to join a new government unless there are major changes to post-Brexit border arrangements, known as the Northern Ireland Protocol, that are opposed by many unionists.
The post-Brexit rules have imposed customs and border checks on some goods entering Northern Ireland from the rest of the U.K. The arrangement was designed to maintain an open border between Northern Ireland and EU member Ireland, a key pillar of the peace process.
But it angered unionists, who maintain that the new checks have created a barrier between Northern Ireland and the rest of the U.K. that undermines their British identity.
In February the DUP’s Paul Givan resigned as first minister as post-Brexit tensions triggered a fresh political crisis in Northern Ireland.
Sinn Fein’s vice-president Michelle O’Neill said the party wanted to work “in partnership with others.”
She also said that with regard to Irish unification, there would be no constitutional change until voters decide on it.
Party leader Mary Lou McDonald indicated on Friday that planning for any unity referendum could come within the next five years.
The full results of the election, which uses a system of proportional representation, were expected later in the weekend.
The new legislators will meet next week to try to form an executive. If none can be formed within six months, the administration will collapse, triggering a new election and more uncertainty.