"Discussions will continue next week to work on the details and to reach agreement on arrangements for the new parliament", it said. "They (the DUP) are going to support us on the big Brexit, economic and security issues facing this country", he said. May's office has said that the most senior Cabinet members - including Treasury chief Philip Hammond, Foreign Secretary Boris Johnson and Home Secretary Amber Rudd - will keep their jobs, but she is expected to shuffle the lower ranks of ministers.
There was no mention of what concessions the DUP may have asked for, amid growing concern about the influence of a party opposed to abortion and gay marriage.
The Labour leader, who has insisted the Conservatives lost the election despite being the largest party, was photographed by Times columnist Giles Coren at the football practice in sunny north London as the Prime Minister grappled with the fallout of losing her majority.
May said Brexit talks would begin on June 19 as scheduled, the same day as the formal reopening of parliament.
They were replaced by Gavin Barwell, a former housing minister who lost his seat in the election.
Mrs May failed to win a majority in the British parliament in an election on Thursday.
"From hubris to humiliation", said the left-leaning Guardian.
Britain's typically right-wing press savaged May over the election outcome, questioning whether she will be able to remain in power after a result that leaves her reliant on uniting rival factions within her party to deliver Brexit.
Several Conservative lawmakers have warned that May can not carry on indefinitely, after throwing away a 17-seat majority in the 650-seat House of Commons.
At the same time Ruth Davidson, leader of the Conservatives in Scotland - where the party reversed the trend in England and gained MPs - has called for a new approach building cross-party support for an "open Brexit".
The Conservatives won 318 seats, down from 331 in 2015 and falling short of an overall majority, after the opposition Labour party under socialist leader Jeremy Corbyn scored hefty gains.
Labour, the main opposition party, won 262.
PROPPING DUP THE TORIES Who are the Democratic Unionist Party and what's in the 2017 DUP manifesto?
"I sought, and to be fair to the prime minister, received a categoric assurance that in talking to the DUP that there would be no suggestion of any rollback on LGBTI rights in the rest of the United Kingdom", she told reporters.
"I could not care less what people get up to in terms of their sexuality".
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.
If she is to succeed in delivering the wishes of the 52 per cent of voters who opted to take Britain out of the European Union a year ago, she must find a way to bridge the differences within her party to pass legislation preparing for and enacting the departure.