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Unable to govern without support after the snap election, she has yet to secure the backing of a eurosceptic Northern Irish party with 10 parliamentary seats.
The outcome of last week's vote has also thrown into doubt what Britain would seek from Brexit talks with the EU, complex negotiations which will have profound implications for the world's fifth largest economy.
May will attend a meeting of the 1922 Committee of Conservative lawmakers on Monday, some of whom have called for her to be ousted.
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| Britain's Prime Minister Theresa May and her husband Phillip arrive at church in Sonning, Britain June 11, 2017. REUTERS/Stefan Wermuth |
However, despite anger from some at the shock result, May's position appears safe, at least for the immediate future.
"I don't detect any great appetite amongst my colleagues for presenting the public with a massive additional dose of uncertainty by getting involved in a self-indulgent Conservative Party internal election campaign," Graham Brady, the 1922 committee chairman, told BBC TV.
"SOFTER BREXIT"
EU talks might not begin on June 19 as expected as May sets out her new policy program that day, Brexit minister David Davis said. The negotiations are supposed to conclude by March 2019 when Britain leaves, an ambitious-looking date even before the election debacle cast doubt on what UK strategy would be.
May had planned a clean break from the EU, involving withdrawal from Europe's single market and customs union but some Conservatives and opponents hope the election shock will lead to a "softer" Brexit, which prioritizes close trade links over controlling immigration.
One of those is Ruth Davidson, the leader of the Scottish Conservatives who helped the party win 12 more seats in contrast to losses elsewhere, one of the few whose personal stature was enhanced by the result.
Ratings agency Moody's and Ireland's prime minister designate Leo Varadkar also said the election made the opportunity of a "soft Brexit" more likely, but Davis downplayed the chances of Britain staying in the single market.
"The interpretation that we have put on it ... is that people voted for three things in essence, control of borders, control of laws, control of money," Davis told BBC radio.
"In order to deliver that you can't do that inside the single market, so what do you do, you try and have the best possible access from outside."
May's spokesman said it remained government policy to cut net migration to under 100,000 and Davis also said walking away without securing a deal with the remaining 27 EU states remained a possibility.
