DUP leader Arlene Foster has said the party has entered discussions with the Conservatives "to explore how it may be possible to bring stability to our nation".
The former Stormont first minister, who led her party to 10 seats in the Westminster election, said the DUP will strive for the best deal for Northern Ireland, its people and an agreement that is best for the United Kingdom.
"The Prime Minister has spoken with me this morning and we will enter discussions with the Conservatives to explore how it may be possible to bring stability to our nation at this time of great challenge," she said.
Ms Foster described her party's resounding victory in Northern Ireland as "truly historic" as the DUP recorded its best ever election result.
Sending a powerful team of 10 MPs to a hung parliament puts the Democratic Unionists in the enviable position of being kingmakers at Westminster.
Mrs Foster, flanked by each one of her representatives in the House of Commons, did not take any questions after confirming plans for talks with the Conservatives.
"Yesterday also represented a great result for the Union. Not just here in Northern Ireland but right across our United Kingdom," she said.
"Those who want to tear apart the Union that we cherish and benefit from so hugely have been sent a clear and resounding message."
"In the days and weeks ahead, it is that Union that will be to the forefront of our minds. The Union is our "guiding star".
"We may represent Northern Ireland constituencies in the House of Commons but we are as seized of the interests of the Kingdom as a whole as we are for our small province.
"I make no apology for saying that the DUP will always strive for the best deal for Northern Ireland and its people. But equally, we want the best for all of the United Kingdom."
Ms Foster described the uncertainty facing the UK, following the recent terror attacks, the close run election and Brexit negotiations on the horizon.
She added: "Our United Kingdom - and indeed our very way of life - are under threat from extremists."
Ahead of the talks with Conservatives, a senior DUP member said any deal will not extend beyond a confidence and supply arrangement.
East Belfast MP Gavin Robinson said his party was in a "fantastic position to deliver for Northern Ireland".
Prime Minister Theresa May has announced that she will work with "friends and allies" in the DUP to enable her to lead a government.
Prior to the 2015 election, with the pollsters predicting a hung parliament, the DUP ruled out a potential formal coalition with the Conservatives, instead indicating its support would be offered in a confidence and supply arrangement from the opposition benches.
Mr Robinson said: "We have essentially got the result we were campaigning for two years ago.
"It didn't materialise then but we campaigned on the basis of a hung parliament two years ago.
"I think that puts us in a fantastic position to deliver for Northern Ireland."
The DUP made its positions clear in the election campaign that it wanted a Tory government.
In a speech cancelled in the wake of the Manchester terror attack, Mrs Foster planned to describe Jeremy Corbyn as "beyond the political pale" because of his past support for Irish republicans.
She attacked the Labour leader's credibility, including warning that it was hard to take him seriously because of his meetings with political representatives of the IRA at the height of the Troubles.
Mrs Foster was due to set out her stall at a meeting of the pro-Brexit Bruges Group in Mayfair on May 22, but pulled the speech after Ariana Grande's concert in Manchester was targeted by a suicide bomber.
The DUP and Sinn Fein dealt a series of devastating blows to their rivals in Northern Ireland to emerge from the General Election stronger than ever.
The two main parties advanced as the Ulster Unionists and SDLP were wiped off the Westminster map.
Sinn Fein's seven MPs are not part of calculations to form a government because the republican party refuses to take its seats in Westminster.
Sinn Fein president Gerry Adams hailed what he described as a historic result for his party.
"Sinn Fein respects the mandate we have received and our electorate who voted in such huge numbers," he said.
"Nationalists and republicans have turned their back on Westminster and accept that the centre of political gravity is now on the island of Ireland.
"The Taoiseach and DUP need to focus on restoring the political institutions.
"Theresa May sought a mandate for Brexit, austerity and the erosion of human rights. She got her comeuppance.
"The Irish government needs to seize the initiative to secure designated special status for the North as part of the Brexit negotiations."