A spokesperson for the Prime Minister has declined to comment on the timing of any talks between the two parties.
Chancellor of the Exchequer: Philip Hammond. But Britain's Saturday newspapers agreed she is just clinging on.
After all 650 seats were declared, the Conservative Party had lost 12 seats, bringing it to a total of 318, while Labour gained 32 to reach 262.
Indeed, the prospect of a "hard" Brexit, by which the United Kingdom leaves with no deal, has shrunk with the Conservative majority, as it's a likely "red line" for the Democratic Unionist Party, the Northern Irish lawmakers May has turned to for support in Westminster.
A senior Conservative lawmaker was in Belfast on Saturday for talks with the DUP, a spokeswoman for May's office said.
Foster did not elaborate on the DUP's wish list of concessions but it will likely try to extract more money from the central government for public services in Northern Ireland. MONDAY, JUNE 19 - Brexit talks begin Talks on Britain's exit from the European Union are due to begin.
But she seems secure for the immediate future, because senior Conservatives don't want to plunge the party into a damaging leadership contest.
However, he acknowledged that the party would have to abandon much of the programme set out in the general election manifesto as it would no longer be able to get it through Westminster.
Labour leader Jeremy Corbyn has urged May to resign, but the PM said at her count in Maidenhead that "it would be incumbent on to assure we have that period of stability, and that is exactly what we will do".
May says it's "a Cabinet that reflects the wealth of talent and experience across the Conservative Party" and "a government that is going to be governing for everyone".
"This is not the time for sharks to be circling".
The Times of London said in an editorial that "the election appears to have been, among other things, a rejection of the vague but harshly worded prospectus for Brexit for which Mrs". I think probably before this election you could have assumed it was going to happen. But not for some time, let's get this clear. We need a Brexiteer.
In another sign of the dangers facing Mrs May, Sunday papers reported that Boris Johnson was either being encouraged to make a leadership bid in an effort to oust her, or actually preparing one - a claim dismissed as "tripe" by the foreign secretary. The DUP won 10 seats.
Defending her party's stance on gay marriage in a recent interview, leader Arlene Foster insisted those who characterised the DUP as anti-gay were wide of the mark.
It has also blocked attempts to change Northern Ireland's strict laws on abortion.
Meanwhile, Sinn Fein accused the DUP of betraying the interests of Northern Ireland - with Stormont leader Michelle O'Neill predicting a confidence and supply deal would "end in tears".
"I think its quite possible there'll be an election later this year or early next year, and that might be a good thing, because we can not go on with a period of great instability", he told the BBC's Andrew Marr on Sunday.
When asked about the possibility of adopting a more reconciliatory relationship with his detractors in Parliament, Corbyn told Marr he would be very receptive to such opportunities.