With no clear winner emerging from Thursday's parliamentary election, a wounded May signalled she would fight on, despite being on course to lose her majority in the House of Commons.
Her Labour rival Jeremy Corbyn said she should step down.
With 633 out of 650 seats declared, the Conservatives had won 308 seats and were therefore no longer able to reach the 326-mark they would need to command a parliamentary majority.
Labour had won 258 seats.
With talks of unprecedented complexity on Britain's departure from the European Union due to start in just 10 days' time, the pound sterling was hit by uncertainty over who would form the next government and over the fundamental direction Brexit would take.
"At this time, more than anything else this country needs a period of stability," a grim-faced May said after winning her own parliamentary seat of Maidenhead, near London.
"If ... the Conservative Party has won the most seats and probably the most votes then it will be incumbent on us to ensure that we have that period of stability and that is exactly what we will do."
After winning his own seat in north London, Corbyn said May's attempt to win a bigger mandate had backfired.
"The mandate she's got is lost Conservative seats, lost votes, lost support and lost confidence," he said.
"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."
Conservative member of parliament Anna Soubry was the first in the party to break cover, calling on May to "consider her position".
"I'm afraid we ran a pretty dreadful campaign," Soubry said.
May had unexpectedly called the snap election seven weeks ago, even though no vote was due until 2020.
At that point, polls predicted she would massively increase the slim majority she had inherited from predecessor David Cameron.
Instead, she risks an ignominious exit after just 11 months at Number 10 Downing Street, which would be the shortest tenure of any prime minister for almost a century.
"Perhaps the most obvious conclusion is that the likelihood of the UK needing to request a delay in the Brexit process has risen substantially," JPMorgan said in a note.
MAY IS TOAST
"Whatever happens, Theresa May is toast," said Nigel Farage, former leader of the anti-EU party UKIP.
May had spent the campaign denouncing Corbyn as the weak leader of a spendthrift party that would crash Britain's economy and flounder in Brexit talks, while she would provide "strong and stable leadership" to clinch a good deal for Britain.
But her campaign unravelled after a major policy u-turn on care for the elderly, while Corbyn's old-school socialist platform and more impassioned campaigning style won wider support than anyone had foreseen.
Political turmoil in Britain is the worst-case scenario for EU leaders who want to press ahead quickly with Brexit talks.
These are due to start on June 19 but now risk being delayed - narrowing the window of time available to clinch a deal before a March 2019 deadline.
"Could be messy for the United Kingdom in the years ahead. One mess risks following another. Price to be paid for lack of true leadership," tweeted former Swedish Prime Minister Carl Bildt, one of the EU's elder statesmen.
Sterling fell by more than two cents against the U.S. dollar after an exit poll showed May losing her majority, though it later recovered some of its losses.
"A hung parliament is the worst outcome from a markets perspective as it creates another layer of uncertainty ahead of the Brexit negotiations and chips away at what is already a short timeline to secure a deal for Britain," said Craig Erlam, an analyst with brokerage Oanda in London.
With the smaller parties more closely aligned with Labour than with the Conservatives, the prospect of Corbyn becoming prime minister no longer seems fanciful.
That would make the course of Brexit even harder to predict.
During his three decades on Labour's leftist fringe, Corbyn consistently opposed European integration and denounced the EU as a corporate, capitalist body.
As party leader, Corbyn unenthusiastically campaigned for Britain to remain in the bloc, but has said that Labour would deliver Brexit if in power, albeit with very different priorities from those stated by May.
"What tonight is about is the rejection of Theresa May's version of extreme Brexit," said Keir Starmer, Labour's policy chief on Brexit, saying his party wanted to retain the benefits of the European single market and customs union.
On a nerve-racking night for the Conservatives, interior minister Amber Rudd held on to her seat by a whisker, while several junior ministers were swept away. In one of many striking moments, the party lost the seat of Canterbury for the first time in a century.
The Conservatives could potentially turn for support to Northern Ireland's Democratic Unionist Party (DUP), a natural ally, projected to win 10 seats.
But Labour had potential allies too, not least the Scottish National Party (SNP) who suffered major setbacks but still won a majority of Scottish seats.
The pro-EU, centre-left Liberal Democrats were having a mixed night. Their former leader, Nick Clegg, who was deputy prime minister from 2010 to 2015, lost his seat.
But former business minister Vince Cable won his back, and party leader Tim Farron held on.
In domestic policy, Labour proposes raising taxes for the richest 5 percent of Britons, scrapping university tuition fees, investing 250 billion pounds ($315 billion) in infrastructure plans and re-nationalising the railways and postal service.
Analysis suggested that Labour had benefited from a strong turnout among young voters.
UKIP saw a collapse in its support, shedding votes evenly to the two major parties instead of overwhelmingly to the Conservatives, as pundits had expected.
"UKIP voters wanted Brexit but they also want change," Farage said.
"They are fundamentally anti-establishment in their attitudes and the vicarâs daughter (May) is very pro-establishment. And I think she came across in the campaign as not only as wooden and robotic but actually pretty insincere."
In Scotland, the pro-independence SNP were in retreat despite winning most seats.
Having won all but three of Scotland's 59 seats in the British parliament in 2015, their share of the vote fell sharply and they lost seats to the Conservatives, Labour and the Liberal Democrats.
The campaign had played out differently in Scotland than elsewhere, the main faultline being the SNP's drive for a second referendum on independence from Britain, having lost a previous plebiscite in 2014.
SNP leader and First Minister Nicola Sturgeon said it had been a disappointing night for her party, while Scottish Conservative leader Ruth Davidson said Sturgeon should take the prospect of a new independence referendum off the table. - Reuters