British Prime Minister Theresa May faced negotiations with a small Northern Irish party to maintain her power after her Conservative Party lost its parliamentary majority in a catastrophic electoral gamble just days before Brexit talks are set to start.

May's Downing Street office said on Sunday she had spoken with the Democratic Unionist Party (DUP), to discuss finalising a deal when parliament is reconvened next week.

"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," Downing Street said in a statement.

"As and when details are finalised both parties will put them forward," it said, referring to May's Conservative Party and the DUP.

The Conservatives won 318 House of Commons seats in the election, eight short of an outright majority. The DUP won 10 seats.

May had called the snap election with a view to increasing the narrow majority she had inherited from her predecessor David Cameron. At the start of the campaign, she was enjoying poll leads of 20 points or more over the main opposition Labour Party.

But after a poor campaign and an unexpectedly stiff challenge from the opposition Labour Party under leader Jeremy Corbyn, her plan went disastrously wrong, leaving her unable to form a sustainable government without DUP support.

The timing is challenging, with Britain due to start negotiating the terms of its exit from the European Union with the bloc's 27 other members on June 19.

The Conservatives now plan to reach a so-called confidence and supply agreement with the DUP, which would involve it supporting a Conservative minority government on key votes in parliament but not forming a formal coalition.

After an initial round of discussions, Downing Street had said on Saturday that the "principles of an outline agreement" had been agreed with the DUP.

The DUP itself later issued a statement saying the talks had been positive, but stopped short of confirming a deal had been sealed.

"The DUP today (Saturday) held discussions with representatives of the Conservative Party in line with Arlene Foster's commitment to explore how we might bring stability to the nation at this time of great challenge," the party said.

"The talks so far have been positive. Discussions will continue next week to work on the details and to reach agreement on arrangements for the new parliament."