The DUP is a far-right and homophobic party in Northern Ireland, who vetoed several votes for same-sex marriage.
The Protestant unionist party also had links with outlawed paramilitary groups during the years of Northern Ireland's "Troubles".
The DUP said earlier on Friday it would not comment on reports that it had agreed to back May's ruling Conservatives.
It would mean the DUP backing the Government on its Budget and prevent it being brought down by motions of no confidence, but could potentially lead to other issues being decided on a vote-by-vote basis.
Downing Street said an outline agreement on a "confidence and supply" arrangement had been reached which will be put to the Cabinet for discussion on Monday.
"Theresa May has been in British politics for quite a long time, but she is not somebody with a huge media profile or who is associated with particular policy positions", Goodwin told ABC News ahead of election day. Together, the Conservatives and the DUP would have 328 seats in parliament, just above the 326 needed. They quit Saturday after becoming a focus of blame for the Conservatives' election disaster.
The European Parliament's top Brexit official called the British election result "yet another own goal" for the Conservative Party and said it will make "already complex negotiations even more complicated".
"What the country needs now is certainty", she said.
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"Gavin will have an important role to play in that".
Liberal Democrats gained four seats to amass 12 MPs, but lost its former leader and ex-deputy prime minister Nick Clegg in perhaps the highest-profile casualty in a night of stunning results. The election, which has overturned all opinion poll projections of a strong Conservative party majority, recorded the highest turnout in 25 years at 68.7 per cent, with almost 32 million of the 46.9 million registered voters casting their ballots.
The Conservatives won more than 13.6 million votes, which is an historically high number, and more than Tony Blair won in all three of his election victories.
"While the DUP supported the "leave" campaign, it is hard to envisage a scenario where a Northern Irish party would support the return of a hard border", said Mr Ryan McGrath, an analyst at Cantor Fitzgerald LP in Dublin.
Several Conservative lawmakers have warned that May can not carry on indefinitely, after throwing away a 17-seat majority in the 650-seat House of Commons.
As Britons awoke to news that Prime Minister Theresa May would have to turn to the Democratic Unionist Party (DUP) for support after unexpectedly losing her parliamentary majority in an election, the Northern Irish party's website crashed under the weight of curiosity.
Downing Street said Chancellor Philip Hammond, Foreign Secretary Boris Johnson, Home Secretary Amber Rudd, Brexit Secretary David Davis and Defence Secretary Sir Michael Fallon would remain in post.
May's party fell short of an overall majority following Thursday's vote, and plans to work with Northern Ireland's Democratic Unionist Party. "Our shared responsibility and urgent task now is to conduct the negotiations on the UK's withdrawal from the European Union in the best possible spirit, securing the least disruptive outcome for our citizens, businesses and countries after March 2019", said Tusk, who chairs summits of European Union leaders.