The result represents a humiliation for May given she called the snap election to increase her majority, an has raised questions over the impact on the UK's exit from the European Union.
May's weakened position in the party rules out big changes to the Cabinet lineup.
May called the election to win explicit backing for her stance on Brexit, which involves leaving the EU's single market and imposing restrictions on immigration while trying to negotiate free trade deal with the bloc.
DUP leader Arlene Foster said she had spoken with Conservative leader May and would start talks on propping up the party, declaring that keeping Northern Ireland in the United Kingdom would be "our guiding star". Conservative seats are now more heavily concentrated in Brexit-supporting areas and most of the party's new English MPs will represent voters who want to leave the European Union as quickly and cleanly as possible.
Speaking as she was re-elected MP for Maidenhead, Mrs May said: "At this time, more than anything else, this country needs a period of stability".
When asked if she would continue her term in office May said, "I said during the election campaign that if re-elected I would intend to serve a full term".
"Ted Heath lost and tried to form another government and tried to get another majority in Parliament".
The result has demolished May's political authority, and she has also lost her two top aides, sacrificed in a bid to save their leader from being toppled by a furious Conservative Party.
It comes after Irish Foreign Minister Charlie Flanagan said an agreement between the Tories and DUP would "not necessarily" undermine the Northern Ireland peace process.
There had been speculation Mr Hammond, the Chancellor, would be vulnerable in a post-election re-shuffle and the decision to leave him in the Treasury was being seen as a sign of her weakness after her Commons majority was wiped out.
Kerber makes history, crashes out in first round
Last week, she made a last-minute decision to play at Roland Garros and says she doesn't feel much pain when playing. Afterwards, several other players reached out to show how excited they were for Kvitova's opening-match win.
The arrangement with the DUP will make governing easier, but it makes some Conservatives uneasy.
The source said the DUP was likely to seek a role in Brexit negotiations but was likely to steer clear of social issues such as abortion and gay rights, where it disagrees with Conservative Party positions.
The DUP won 10 seats, which would mean the Conservatives would have support from a majority of 328 deputies if they confirm the confidence-and-supply arrangement with the DUP.
A deal between the government and the DUP could also unsettle the precarious balance between Northern Ireland's British loyalist and Irish nationalist parties, whose power-sharing administration in Belfast collapsed earlier this year.
"The Taoiseach indicated his concern that nothing should happen to put the Good Friday Agreement at risk and the challenge that this agreement will bring", the Irish government said in a statement. "Any British government is not a neutral observer on these matters".
As she retreated inside No. 10, it was claimed the Prime Minister had to be told to apologise to her defeated MPs and ministers, by the chairman of the Tory backbench 1922 Committee, Graham Brady.
"There's a possibility of voting the Queen's Speech down and we're going to push that all the way".
"We want to end austerity and invest in this country and that's what we're going to do".
The prime minister was the alpha and the omega of the Conservative campaign, which emblazoned her name in huge lettering on its posters and buses.
A BBC projection put the Tories on 43% overall, about six points up on David Cameron's result in 2015, and Labour on 40%, spectacularly outpolling Ed Miliband and Gordon Brown's results and even racking up more votes than Tony Blair did when he won power in 2005. "This is still on".
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