The support of DUP, with 10 MPs, is crucial to the continuance in office of the minority government, after the Conservative Party fell short by eight of the majority mark of 326 in the 650-member House of Commons in Thursday's election.
Flanked by her 10 MPs, the DUP leader was vague about what her party will request from the Conservatives in exchange for keeping Mrs May in Downing Street.
Scottish Conservative leader Ruth Davidson said she has received assurances from the Prime Minister over gay rights should the Tories do a deal with the party.
The humiliating result has heaped pressure on May to resign, but she says she will stay and lead Britain during exit talks with the European Union.
He said: "The actions of this government will have profound implications for the Brexit negotiations and the future of our country".
She said she "obviously wanted a different result" and felt "sorry" for colleagues who lost their seats.
The arrangement with the DUP will make governing easier, but it makes some Conservatives uneasy.
European Union defence plans aim to support NATO -Juncker
Both Mogherini and Juncker said security and defense are among top priorities of citizens in all European Union countries. He said the United States is "no longer interested in guaranteeing Europe's security in our place".
Those contrasting views were played out during the election, with the DUP urging voters to strengthen the Union and Sinn Fein encouraging supporters to add momentum to their campaign for a border poll.
Northern Ireland is the only part of the U.K.in which same-sex marriage is illegal.
DUP leader Arlene Foster confirmed that she had spoken to May and that they would speak further to "explore how it may be possible to bring stability to this nation at this time of great challenge", the BBC reported.
"While I have always been careful never to threaten a Bosnian type situation in Northern Ireland, it is clear that others foresee such a possibility".
The Prime Minister's situation appeared precarious as Conservative former minister Anna Soubry said she should "consider her position" and take personal responsibility for a "dreadful" campaign and a "deeply flawed" manifesto after choosing to go to the country three years early in the hope of extending her majority.
The DUP has a consistently anti-abortion stance and has repeatedly opposed attempts to legalise it. "When it becomes a matter for me is when people try to redefine marriage". The Labour Party, led by Jeremy Corbyn, did much better than most forecasters predicted, and has 261 seats at last count.
But a deal between the DUP and Conservative Party would risk destabilising the political balance in Northern Ireland by increasing the influence of pro-British unionists who have struggled for years with Irish nationalists who want Northern Ireland to join a united Ireland. "May fights to remain PM", said the front page of the Daily Telegraph, while the Times of London said: "May stares into the abyss".
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