But May made clear she would struggle on and seek to govern after receiving Unionist assurances.
After a brief meeting with Queen Elizabeth II at Buckingham Palace, May said this morning the new government will guide Britain's exit talks from the European Union, which are set to begin in just 10 days.
Labour's Corbyn told the Sunday Mirror newspaper he saw a route to power himself, although it was not clear how he would command the support of a majority of members of parliament.
"The election result was a comprehensive rejection of the Tory plans for an extreme Brexit - and single market membership must now be back on the table", he said.
The DUP has reportedly promised to lend the Tories their 10 votes - not in coalition but as a looser arrangement.
Labour leader Jeremy Corbyn has insisted "I can still be prime minister" as he vowed to fight Theresa May's attempt to run a minority government "all the way".
This partnership is taking shape at a particularly sensitive time in the always delicate politics of Northern Ireland.
From the statement, it appears as though May will be forming an official coalition between the Conservatives and the Unionists.
British Prime Minister Theresa May's two chiefs of staff have resigned in the wake of the Conservative Party's disastrous election result.
If May stays in the longer term she will likely be forced to open up No 10 to a more consultative operation, having previously preferred to work with a tight-knit coterie of close advisers.
During the campaign, she said she prided herself on sometimes being a "bloody hard woman". Many others have been less vocal, but with 12 fewer Conservative seats in parliament than before the election, you can be sure many are smarting if not seething, meaning a leadership challenge could soon be on the cards.
At the start of the campaign it looked as if she might pull off a landslide victory, but opinion polls showed the race tightening, and May came under criticism for running an aloof campaign that took the voters for granted. The Conservatives had to backtrack on plans to make the elderly pay more for residential and social care.
For its part, the European Union urged May on Friday to start Brexit talks as quickly as possible, but warned of complications ahead.
May's Downing Street office had announced on Saturday that the "principles of an outline agreement" had been agreed with the DUP, only for the smaller party to contradict that account hours later.
The result leaves Britain in a less certain position regarding its Brexit negotiations.
Seeking to capitalise on high popularity ratings, the Conservative Party leader and prime minister called for a snap election despite her initial pledges not to, urging voters to give her a stronger mandate to lead the UK's Brexit negotiations.
If the June 8 General Election ends in a hung parliament, it could be a matter of days or weeks before the final form of the next government is settled. But in one of the most sensational nights in British electoral history, a resurgent Labour Party denied her an outright win, throwing the country into political turmoil as no clear victor emerged.
"Yet another own goal, after Cameron now May, will make already complex negotiations even more complicated", tweeted Guy Verhofstadt, the former Belgian premier who is the European Parliament's point man for the Brexit process. Ladbrokes reckoned the odds were 2/1 for a second vote in 2017.
In the late stages of the campaign, Britain was hit by two Islamist militant attacks that killed 30 people in Manchester and London, temporarily shifting the focus onto security issues.