"We will fulfil the promise of Brexit together and over the next five years build a country in which no one, and no community, is left behind".
The DUP and Irish nationalists Sinn Fein are due to restart talks to form a new power-sharing government in Northern Ireland and avoid devolved power reverting to the British parliament in London for the first time in a decade.
Downing St. said the Cabinet will discuss the agreement on Monday.
It's on those social issues that the DUP may be seen in London as an uncomfortable partner for the Conservatives, with stances that are odds with the more liberal views prevalent in the rest of the UK.
May called the snap election in April - three years earlier than required by law - seeking to strengthen her government's mandate ahead of the Brexit talks.
Sunday's newspapers were unsparing, with The Observer writing: "Discredited, humiliated, diminished".
Challenged if Labour could have won under another leader, Mr Leslie said: "I've never known a more beatable Prime Minister than Theresa May - brittle, I think very, very wobbly and shaky indeed".
Bookies also slashed odds on Foreign Secretary Boris Johnson taking over as PM with the former London Mayor rumoured to be making a bid for the leadership.
Former Treasury chief George Osborne - who was sacked by May a year ago - called May a "dead woman walking", and opposition leader Jeremy Corbyn said he was ready to contest another election at any time.
"This is still on", he said, adding he would vote down the government's programme when it comes before parliament this month.
This would include an emphasis on jobs in the Brexit talks and a guarantee of the rights of European Union nationals to stay in UK.
Under pressure from Conservative cabinet ministers, May accepted the resignation of her two top aides, her co-chiefs of staff Nick Timothy and Fiona Hill, on Saturday.
"She wanted a mandate", he said, "well the mandate she has got is lost Conservative seats, lost votes, lost support and lost confidence". The Daily Mail screamed: "Gamble That Backfired".
The British currency lost as much as 3 cents against the dollar by Friday as the results confirmed exit poll predictions that Prime Minister Theresa May had failed in her gambit to gain a stronger majority for those Brexit talks.
With almost all votes counted, the Conservative Party has 318 seats, according to the BBC.
"I asked for a categoric assurance that if any deal or scoping deal was done with the DUP there would be absolutely no rescission of LGBTI rights in the rest of the United Kingdom, in Great Britain, and that we would use any influence that we had to advance LGBTI rights in Northern Ireland", said the MP, who is a lesbian.
"The UK desperately needs to attract investors if it is to improve its ailing infrastructure yet the political uncertainty in which we now find ourselves is precisely what puts off investors and will make our infrastructure problems more hard to solve", he said.
Senior Tories have also expressed concern over the prospect of closer links with the DUP - with one MP, Sarah Wollaston, tweeting: "I will always oppose the death penalty & would resign if others imposed it".
The Conservatives, as the largest party, have the best chance of achieving this, especially with the support of the Democratic Unionist Party, a natural ally.
EU Council President Donald Tusk says that Britain should look to start discussions to leave the European Union as soon as possible or it risks crashing out of the bloc with no deal.
Sinn Fein does not take its seats in the British parliament, with MPs refusing to swear allegiance to the British head of state, Queen Elizabeth II.