With all 90 seats now declared after Thursday's snap election, the DUP has 28 seats, just one ahead of Sinn Fein, and unionist parties now no longer hold a majority of seats overall. Going into the vote, the DUP held a 10-seat advantage.
"Let us now move forward with hope, hope that civility can return to our politics," Reuters news agency quoted former First Minister Arlene Foster of the DUP as telling supporters after the votes were counted. "There is work to be done to quickly mend the relationship, which has been frayed by the discord of this election."
Sinn Fein President Gerry Adams welcomed the results, saying: "The Sinn Fein vote in this election was for equality, respect and integrity in government. It was a vote against Brexit and for the North to have a designated special status within the EU."
Under Northern Ireland's complex power-sharing agreement -- established as part of the peace process
-- a new government must be run jointly by unionist and nationalist parties. The DUP and Sinn Fein will now enter power-sharing negotiations to form a new government at Stormont.
If they are not able to come to an agreement within three weeks, then devolved power could be returned to the UK Parliament in Westminster for the first time in 10 years, Reuters said.
James Brokenshire, the UK government's secretary of state for Northern Ireland, said in a statement Saturday that the election had "demonstrated the clear desire by the overwhelming majority of people in Northern Ireland for inclusive devolved government."
He added, "Everyone now has a shared responsibility to engage intensively in the short period of time that is available to us, to ensure that a strong and stable administration is established."
The snap election, called less than a year after the last ballot, was triggered by the resignation in January of Irish republican leader Martin McGuinness
as deputy first leader of Northern Ireland.
McGuinness led Northern Ireland's government in coalition with Foster but announced his decision to resign after she refused to step aside pending an inquiry into the handling of a botched green energy program.
Sinn Fein, a party primarily supported by Catholic Irish nationalists, wants Northern Ireland to secede from the UK and become part of the Republic of Ireland. The DUP, primarily supported by Protestants, wants the region to remain a part of the United Kingdom.
The United Kingdom is made up of England, Scotland, Wales and Northern Ireland. A majority in Northern Ireland voted in favor of the United Kingdom remaining part of the European Union in last year's Brexit referendum