Mrs May is to stay in office with the support of her "friends" in the Democratic Unionist Party (DUP) after the Conservatives failed to win a majority in the snap election she called. With results declared for almost all of the 650 seats, Conservatives won 318 while the opposition Labour secured 262, leaving neither party anywhere close to the 326 seats required for an overall majority.
"And as I reflect on the results, I will reflect on what we need to do in the future to take the party forward".
Davidson, one of the few Conservatives to emerge as a victor from the election after she increased the party's presence in Scotland, said she had demanded, and received, "categoric assurance" from May that the policy would not change.
Instead, she risked an ignominious exit after just 11 months in the post, which would be the shortest tenure of any prime minister for nearly a century.
May called an election three years ahead of schedule, at a time when her party was well ahead in the polls.
Corbyn also said there's enough opposition in Parliament and in May's own party to topple the government. Conservatives continue to be the largest party in the UK.
She has led a Conservative resurgence in Scotland, providing crucial backing to May's slender majority and dealing a severe blow to the separatist Scottish National Party (SNP), whose number of seats plunged to 35 from 56.
Mr Corbyn took advantage by agreeing to a debate at the last minute - leaving her with a Hobson's choice of either looking too scared to join him or as though she was responding to his instructions.
May experienced a gradual slide during the campaign period, in which a wide gap between the Conservatives and Labour narrowed.
The Tories, as they are commonly known in the United Kingdom, will now have to govern as a minority party, or try to form a coalition government, or force another general election.
With Brexit talks due to start in just 10 days, Brussels appeared to be braced for them to be pushed back. Instead, her decision to hold an election has given her government a weaker rather than stronger hand in the negotiations and in parliament and her "strong and stable" mantra became a joke.
May had advocated a "hard Brexit" - a withdrawal that includes a clean break from the European Union's single market and customs union.
"I want the Conservative party to succeed, I want the Conservative party leader to succeed and I want us to be in government".