Theresa May has said she will form a government with the support of the Democratic Unionists that can provide “certainty” for the future.
Speaking after visiting Buckingham Palace, she said only her party had the “legitimacy” to govern after winning the most seats and votes.
She said she would join with “friends and allies” in the DUP to take forward Brexit, saying: “Let’s get to work”.
The Tories are eight seats short of the 326 needed to command a majority.
After losing her majority, Labour’s Jeremy Corbyn has urged the prime minister to quit, saying he is “ready to serve” himself, while Lib Dem leader Tim Farron said she “should be ashamed” and should resign “if she has an ounce of self respect”.
In a short statement outside Downing Street, which followed a 25-minute audience with The Queen, Mrs May said she intended to form a government which could “provide certainty and lead Britain forward at this critical time for our country”.
Referring to the “strong relationship” she had with the DUP but giving little detail of how their arrangement might work, she said the government would “guide the country through the crucial Brexit talks” that begin in just 10 days’ time.
“Our two parties have enjoyed a strong relationship over many years,” she said.
“And this gives me the confidence to believe that we will be able to work together in the interests of the whole United Kingdom.”
The BBC’s Laura Kuenssberg said the PM had returned to No 10 a “diminished figure”, having ended up with 12 fewer seats than when she called the election in April.
She had called the election with the stated reason that it would strengthen her hand in negotiations for the UK to leave the EU – the talks are due to start on 19 June.
The Tories are forecast to end up with 319 seats, ahead of Labour on 261, the SNP 35 and the Lib Dems on 12. The DUP won 10 seats.
Combined, the Tories and the DUP would have 329 MPs in the Commons.
Given the seven Sinn Fein MPs are unlikely to take their seats, such an alliance would enjoy a slightly larger working majority but short of that which Mrs May enjoyed before the election.
Mrs May earlier said the country needed “stability” with the start of Brexit negotiations 10 days away.
It is thought Mrs May will seek some kind of informal arrangement with the DUP that could see it “lend” its support to the Tories on a vote-by-vote basis, known as “confidence and supply”.
The DUP has met to discuss what it has said is a “messy” situation. A DUP source confirmed soundings had been made, but nothing formal had been agreed. Talk of an agreement was described as “premature”.
The Conservatives have argued in the event of a hung Parliament, Mrs May gets the opportunity to form a government first, as her predecessor David Cameron did in 2010 when there was also no clear winner but the party had comfortably more seats than their nearest rival.
Labour has said it is also ready to form a minority government of its own, after far exceeding expectations by picking up 29 seats in England, Wales and Scotland.
But even if it joined together in a so-called progressive alliance with the SNP, Lib Dems, Green Party and Plaid Cymru, it would only reach 313 seats – short of the 326 figure needed.