On Friday she visited the Queen and was granted permission to form government.
The Tories are eight seats short of the 326 needed to command a majority.
The Democratic Unionist Party is the biggest unionist party in Northern Ireland - that is, it is against Ulster becoming part of the Republic of Ireland.
Her Labour rival Jeremy Corbyn, once written off by his opponents as a no-hoper, said May should step down, and that he wanted to form a minority government.
"I would have thought that's enough to go, actually, and make way for a government that will be truly representative of all of the people of this country".
"What the country needs more than ever is certainty, and having secured the largest number of votes and the greatest number of seats, it is clear only the Conservative and Unionist Party has the legitimacy and ability to provide that certainty".
Britons woke up to a hung parliament this morning after May's Conservatives failed to clinch an overall majority, in a shock turnaround from polls early in the campaign that had her on track to trounce Jeremy Corbyn's Labour party.
Stressing that her party had won the maximum votes and emerged as the single largest party, she claimed that only the Tories can provide the "certainty" needed to guide the country through crucial Brexit talks that begins with the European Union on June 19.
However, there was better news for the party as Sir Vince Cable, a former business minister in the coalition government, won back his Twickenham seat from the Conservatives with a majority of 9,762.
Murray into semi-finals after taming Nishikori
The momentum of the match switched sharply after umpire Carlos Ramos penalised Murray the loss of a serve for a time violation. None of the women still playing for the French Open title has ever won a Grand Slam tournament.
Today the EU's chief Brexit negotiator Michel Barnier said talks should begin "when the United Kingdom is ready".
As at 10.30am United Kingdom time (9.30 GMT), with one seat as yet undeclared, the Conservatives had 318 parliamentary seats, Labour 261, Scottish National Party (SNP) 35, Liberal Democrats 12, DUP 10, and others 13. It means those 10 MPs will lend her their support on key votes so she gets things through.
However, John Rowland, executive director and political advisory specialist at consultancy firm Cicero Group said that working with the DUP may present difficulties for May's Brexit plans.
A DUP source was reported as saying: "We want there to be a government". "That is what people voted for last June, that is what we will deliver".
Foreign Secretary Boris Johnson, often tipped as a potential successor to Mrs May as Tory leader, said: "We've got to listen to our constituents and listen to their concerns".
The Northern Irish party said they would consider coming to a "confidence and supply" agreement.
The party also wants more defence spending, an increase in the minimum wage, reductions to household energy bills and the maintenance of the "triple lock" ensuring increases in pensions that Mrs May abandoned before the election, according to its manifesto.
UKIP spearheaded the push for Brexit and Nuttall insisted that the party would still remain influential as Britain heads into divorce talks with the European Union.
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