She also apologised to her colleagues who had lost seats as a outcome.
The Conservatives won 318 seats, eight short of the 326 needed for a bare majority, and Mrs May announced that she meant to form a government with the Democratic Unionist Party (DUP) of Northern Ireland, which won 10 seats.
"The Conservatives have not yet broken the British system of democracy, but through their hubris and incompetence they have managed to make a mockery of it", it said in an editorial.
MARTIN: We're seeing that there are calls for Theresa May to resign.
But he has responded in typically colourful fashion, tweeting: "Mail on Sunday tripe - I am backing Theresa may".
A "winnowed out" Queen's Speech next Monday is expected to contain a statement about school funding, according to Graham Brady, chairman of the influential Conservative Party backbench 1922 Committee. He said a new election might be necessary later this year or early in 2018.
In short, Mrs May's troubles are far from over; on the contrary, the internal wars can break out at any time in the fragile hierarchy of the party. "Yet it has failed to win a majority in five of the past six general elections and it has left the country all but ungovernable as a outcome of two extraordinary miscalculations".
"Mrs May is now fatally wounded", The Times wrote. It was three years before the next scheduled election, and the conservatives already had a secure, if small, majority.
The resignation of two of her closest aides on Saturday reflects the pressure she is under from the influential figures in the party, who are ready to mount a leadership challenge, when they sense the first opportunity to do so.
May's Tories, Northern Ireland's DUP Reach Deal to Prop Up Government
Scottish Conservative leader Ruth Davidson said Sturgeon should take the prospect of a new independence referendum off the table. Conservative MP Sarah Wollaston said on Twitter: "I will always oppose the death penalty & would resign if others imposed it".
Analysts say May's electoral debacle could reopen what had seemed largely a closed debate - both with pro-EU members of Parliament trying to take advantage of the prime minister's weakness and Euro-skeptic government ministers threatening her if she dares water down a Brexit deal. But the party still won the largest number of seats and votes - with 318 seats and 12,667,213 votes (42.8% of the overall vote).
The outcome risks upsetting the political balance in Northern Ireland by aligning London more closely with the pro-British side in the divided province, and increases the chance that Britain will fall out of the European Union in 2019 without a deal.
On Brexit, the DUP supports leaving the European Union but opposes a return to a "hard" border with Ireland, which could happen if May carries through her threat to walk away from the talks rather than accept a "bad deal".
Talks between her party and the DUP progressed on Saturday after Tory Chief Whip Gavin Williamson was sent to Belfast to negotiate a deal.
"She might start off doing that but the Conservatives might well replace her mid-stream", he told the Associated Press news agency. But "we know when they must end".
"Other personnel issues are for other days", she said when asked about their future.
"Everybody is positioning themselves", said Anand Menon, professor of European politics and foreign affairs at Kings College London.
"Honestly, it feels nearly like she is nearly not aware of what has happened in the last 24 hours", Conservative MP Heidi Allen told LBC radio.
Downing Street said it hopes to finalize the deal next week, after Parliament resumes sitting.
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