The Conservative leader has been warned that her days are numbered after calling Thursday's vote three years early, only to lose her majority in parliament.
"I don't think there is any great appetite either for a leadership contest or, the public will be relieved to hear, for a general election", he added.
She insisted she would press ahead with Brexit talks, which are to begin in 10 days.
May put on a courageous face following Thursday's vote, expressing sorrow for the MPs who lost their seats, but refusing to acknowledge how her election gamble backfired.
The Scottish National Party remained the biggest party in Scotland but lost 21 seats, its success heavily diminished in comparison to its 2015 general election performance when it won 56 out of 59 Scottish seats.
The statement came as Mrs May's own MPs sharpened knives against her, and a jubilant Jeremy Corbyn demanded she make way for him to become PM.
She is seeking a so-called confidence and supply deal, which would involve the DUP supporting the Conservatives on key votes but not joining a formal coalition.
The DUP, which won 10 seats, said it is ready to talk with May about supporting her government, although such an alliance would be far from straight forward. "It's just how long she's going to remain on death row", former Conservative finance minister George Osborne, who was sacked by Ms May when she became Prime Minister a year ago, told the BBC.
But her party is deeply divided over what it wants from Brexit, and the election result means British businesses still have no idea what trading rules they can expect in the coming years.
In a pooled broadcast interview, Mrs May hinted she could be prepared to sacrifice them to appease her critics once she has completed her ministerial appointments.
British PM under fresh pressure as top aides quit
British Prime Minister Theresa May is making appointments to her Cabinet as she tries to shore up authority undermined by a poor election result.
"What the country needs more than ever is certainty", she said.
His party "didn't win the election", Corbyn says, but he is prepared to continue resisting the Conservative agenda - especially what's known as "hard Brexit", a clean break with the European Union and departure from its single market system.
May's two top aides, Nick Timothy and Fiona Hill, announced they had quit on Saturday, following sustained criticism of the campaign within the party.Britain's typically pro-Conservative press savaged May on Saturday and questioned whether she could remain in power, only two months after she started the clock ticking on the two-year European Union divorce process.
A deal between the government and the DUP could also unsettle the precarious balance between Northern Ireland's British loyalist and Irish nationalist parties, whose power-sharing administration in Belfast collapsed earlier this year.
The DUP also opposes abortion.
Other senior Conservatives however warned against a leadership challenge with Iain Duncan Smith saying it would be a "grave error".
Sinn Féin's leader in Northern Ireland Michelle O'Neill said the DUP had "betrayed the interests of the people" there and the new arrangement would "end in tears".
"I am going to be backing her, and absolutely everybody I'm talking to is going to be backing her too", Johnson later told Sky News.
The border between Northern Ireland and the Republic of Ireland is sure to be a hot topic.
The politicians who've felt the wrath of voters include Home Secretary Amber Rudd, who clings to her seat by just 300 votes. They quit Saturday after becoming a focus of blame for the Conservatives' election disaster.
Comments