Downing Street said an outline agreement on a "confidence and supply" arrangement had been reached which will be put to the Cabinet for discussion on Monday.
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.
"We will welcome any such deal being agreed, as it will provide the stability and certainty the whole country requires as we embark on Brexit and beyond".
Senior party figures have cautioned against any immediate leadership challenge, saying it would cause only further disruption as Britain prepares to start the Brexit talks as early as June 19.
Such a result would leave Labour as the largest party in parliament with Corbyn the favourite to lead a minority or coalition government.
Timothy said the party hadn't noticed the surge in Labour support "because modern campaigning techniques require ever-narrower targeting of specific voters, and we were not talking to the people who made a decision to vote for Labour".
"I don't think Theresa May and this government have any credibility". But this ambitiousness not only cost them their parliamentary majority, but May had also lost two of her closest aides, Nick Timothy and Fiona Hill.
She called the snap election to win a clear mandate for her plan to take Britain out of the EU's single market and customs union in order to cut immigration.
British PM fights for survival ahead of Brexit talks
Former minister Ed Vaizey indicated that Tory MPs were actively discussing Mrs May's position using the WhatsApp messaging system. The turmoil engulfing May has increased the chance that Britain will fall out of the European Union in 2019 without a deal.
The resignations of Timothy and Hill, on whom May had been heavily reliant since her previous job at the interior ministry, will be a personal blow. Timothy - a combative character who one former colleague said had helped create a "toxic" atmosphere at the heart of the government - said he took responsibility for the Conservative manifesto, including a plan for elderly social care that caused a backlash.
The Lib Dems were on seven per cent, while Ukip was up one on three per cent. The Conservatives won 318 out of 650 seats - throwing away a 17-seat majority.
Irish Foreign Affairs Minister Charlie Flanagan said Ireland was keen for Brexit talks to start and to ensure the process of Britain leaving the European Union did not have an adverse impact on Northern Ireland's fragile peace process.
Several hundred people - many of them Labour voters - protested in central London against the alliance, with chants of "racist, sexist, anti-gay, the DUP has got to go".
But shadow chancellor John McDonnell said he believes there is a majority in Parliament to maintain the winter fuel allowance and "triple lock" state pension guarantee, two policies the Conservatives proposed changing in their manifesto.
Joining forces with the hardline Protestant party also threatens London's neutrality in Northern Ireland, which is key to the delicate balance of power in a province once plagued by violence.
But the wooing of the DUP risks upsetting the political balance in Northern Ireland by aligning London more closely with the pro-British side in the divided province, where a power-sharing government with Irish nationalists is now suspended.
He said his party would seek to vote down May's Queen's Speech, or programme for government, when she presented it to parliament.