"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."
From the EU's perspective, the upset in London meant a possible delay in the start of the talks and an increased risk that negotiations would fail.
"We need a government that can act," EU Budget Commissioner Guenther Oettinger told German broadcaster Deutschlandfunk.
"With a weak negotiating partner, there's a danger that the negotiations will turn out badly for both sides."
Conservative member of parliament Anna Soubry was the first in the party to disavow May in public, calling on the prime minister 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.
"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.
In the late stages of the campaign, Britain was hit by two Islamist militant attacks in less than two weeks that killed 30 people in Manchester and London, temporarily shifting the focus onto security issues.
That did not help May, who in her previous role as interior minister for six years had overseen cuts in the number of police officers.
With the smaller parties more closely aligned with Labour than with the Conservatives, the prospect of Corbyn becoming prime minister no longer seems fanciful.
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.
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.
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.
