"Irrespective of religious, political or social backgrounds, my commitment is to make politics work."
O'Neill stressed it was imperative for Northern Ireland's politicians to come together next week to form an executive — the devolved government of Northern Ireland. If none can be formed within six months, the administration will collapse, triggering a new election and more uncertainty.
There is "space in this state for everyone, all of us together," O'Neill said.
"There is an urgency to restore an executive and start putting money back in people's pockets, to start to fix the health service. The people can't wait."
While the Sinn Fein win signals a historic shift that shows diminishing support for unionist parties, it's far from clear what happens next because of Northern Ireland's complicated power-sharing politics and ongoing tussles over post-Brexit arrangements.
Under a mandatory power-sharing system created by the 1998 peace agreement that ended decades of Catholic-Protestant conflict, 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.
Those post-Brexit rules, which took effect after Britain left the European Union, have imposed customs and border checks on some goods entering Northern Ireland from the rest of the UK. The arrangement was designed to keep an open border between Northern Ireland and EU member Ireland, a key pillar of the peace process.
But the rules angered many unionists, who maintain the new checks have created a barrier between Northern Ireland and the rest of the UK that undermines their British identity. In February, the DUP's Paul Givan resigned as the first minister as post-Brexit tensions triggered a fresh political crisis in Northern Ireland.
DUP leader Jeffrey Donaldson said he would announce next week whether he will return to the government.
"We will consider what we need to do now to get the action that is required from the government. I will be making my decision clear on all of that early next week," he told the BBC.
Saturday's results bring Sinn Fein's ultimate goal of a united Ireland a step closer, although the party kept unification out of the spotlight this year during a campaign dominated by the skyrocketing cost of living.
O'Neill has said there would be no constitutional change on Irish unification until voters decide on it.
Sinn Fein leader Mary Lou McDonald indicated on Friday planning for any unity referendum could come within the next five years.
Polling expert John Curtice, a professor of political science at the University of Strathclyde, said Northern Ireland's latest electoral results were a legacy of Brexit.
"The unionist vote has fragmented because of the divisions within the community over whether or not the Northern Ireland Protocol is something that can be amended satisfactorily or whether it needs to be scrapped," he wrote on the BBC website.
Persuading the DUP to join a new government and pressing the EU to agree to major changes in post-Brexit arrangements would pose a headache for British Prime Minister Boris Johnson, Curtice added. Johnson's own Conservative party lost at least 450 seats in Thursday's local election.
Britain's Conservative government says the Brexit customs arrangements cannot work without unionist support in Northern Ireland. Johnson has threatened to unilaterally suspend the Brexit rules if the EU refuses to change them.
