She made the comments after visiting Queen Elizabeth II at 1130 GMT (2130 AEST) and asking for permission to form a new government.
"I have just been to see Her Majesty the Queen and I will now form a government -- a government that can provide certainty and lead Britain forward at this critical time for our country," she said after returning from Buckingham Palace to her Downing Street office in London.
The Conservative leader had called Thursday's snap election in a bid to extend her majority and strengthen her hand in the EU divorce negotiations, but her gamble backfired spectacularly.
Her centre-right party came first but lost its majority in parliament, meaning it is likely to have to secure the support of Northern Ireland's Democratic Unionist Party (DUP) and its 10 extra seats to push it over the line.
Sterling sank against the dollar and the euro on Friday as investors questioned who was now going to control the Brexit process.
EU President Donald Tusk urged Britain not to delay the Brexit talks, warning that time was running out to reach a divorce deal to end four decades of membership.
"We don't know when Brexit talks start. We know when they must end. Do your best to avoid a 'no deal' as result of 'no negotiations'," Tusk wrote on Twitter.
May faced pressure to quit after a troubled campaign overshadowed by two terror attacks, but said Britain "needs a period of stability" as it prepares for the complicated process of withdrawing from the European Union.
'Lost confidence'
But Leftist opposition leader Jeremy Corbyn, whose Labour party surged from 20 points behind in the opinion polls, told May to quit, saying she had "lost votes, lost support and lost confidence".
Tory supporter Nick, 31, blamed the defeat on May's "arrogance".
"It serves her right. Whoever takes over has to understand campaigning is important," he told AFP in London.
With one constituency still to be declared, the Conservatives were on 318 seats -- down from 331 at the 2015 election -- while Labour was on 261, up from 229.
"We are ready to serve this country," Corbyn said, but his party does not have enough potential partners to form a viable minority government.
May, a 60-year-old vicar's daughter, is now facing questions over her judgement in calling the election three years early and risking her party's slim but stable working majority of 17.
'Weak negotiating partner'
The result is "exactly the opposite of why she held the election and she then has to go and negotiate Brexit in that weakened position", said Professor Tony Travers of the London School of Economics university.
Newspapers reflected the drama, with headlines such as "Britain on a knife edge", "Mayhem" and "Hanging by a thread".
In a night that has redrawn the political landscape once again, the UK Independence Party (UKIP), which won 12.6 percent of the vote two years ago and was a driving force behind the Brexit result, lost millions of voters, triggering the resignation of leader Paul Nuttall.
The Scottish National Party of First Minister Nicola Sturgeon, which has dominated politics north of the border for a decade and called for a new independence vote after Brexit, lost 21 of the 56 seats it won in 2015.
'Another layer of uncertainty'
May, who took over after last year's Brexit referendum, began the formal two-year process of leaving the EU on March 29, promising to take Britain out of the single market and cut immigration.
Seeking to capitalise on sky-high popularity ratings, she called the election a few weeks later, urging voters to give her a stronger mandate.
Officials in Brussels were hopeful the election would allow her to make compromises, but this has been thrown into question by the prospect of a hung parliament.
"It creates another layer of uncertainty ahead of the Brexit negotiations," said Craig Erlam, senior market analyst at OANDA currency traders.
Despite campaigning against Brexit, Labour has accepted the result but promised to avoid a "hard Brexit", focusing on maintaining economic ties with the bloc.
Barely a month ago, the centre-left party seemed doomed to lose the election, plagued by internal divisions over its direction under veteran socialist Corbyn.
But May's botched announcement of a reform in funding for elderly care, plus a strong grassroots campaign by Corbyn which energised the youth vote, gave him momentum.
Terror attacks
Britain has also been hit with three terror attacks since March, and campaigning was twice suspended.
A suicide bomber blew himself up outside a pop concert in Manchester on May 22, killing 22 people.
Last Saturday, three assailants mowed down pedestrians and launched a stabbing rampage around London Bridge, killing eight people before being shot dead by police.
The attacks led to scrutiny over May's time as interior minister from 2010 to 2016, particularly since it emerged that some of the attackers had been known to police and security services.
