The DUP say talks with the Conservative Party over supporting a minority government will continue next week.
An announcement by Downing Street on Saturday suggested an agreement had already been reached, but both parties released subsequent statements that said talks would continue.
"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 talks so far have been positive," a DUP statement issued on Sunday morning read.
"Discussions will continue next week to work on the details and to reach agreement on arrangements for the new Parliament."
Earlier it was reported that Conservative Party chief whip Gavin Williamson would hold talks with the DUP in Belfast.
It was expected the parties would enter into an arrangement on a 'confidence and supply' basis.
However, ITV political editor Robert Peston had earlier said Theresa May preferred a more formal coalition, in the interests of stability.
A Downing Street spokesman said: “The Chief Whip is in Belfast holding talks with the DUP on how best they can provide support to the Government.
“We will not be providing a running commentary.”
It is understood that Mr Williamson was meeting the DUP's chief whip Sir Jeffrey Donaldson.