The British government says talks have been positive
British Prime Minister Theresa May will meet DUP leader Arlene Foster on Tuesday, after Downing Street mistakenly announced an agreement with the party.
Ms Foster says her party had "very good" discussions with the UK government Chief Whip Gavin Williamson, who was sent by Mrs May to Belfast to negotiate a deal to keep the Conservatives in power.
She added she will continue discussions to "bring stability to the nation" with Mrs May in London on Tuesday.
It comes after the DUP denied it had reached a "confidence and supply" deal with the Conservatives - despite Downing Street announcing an agreement had been clinched.
Sources said that account of the talks had been issued in error.
On the DUP's approach to discussions, Ms Foster said: "I'm not going to negotiate over the airwaves but what I will say is that we will of course act in the national interest and do what is right for the United Kingdom as a whole and of course Northern Ireland in particular.
"There's been a lot of hyperbole about the DUP since Thursday, a lot of things said, a lot of people who really don't know what we stand for but just to be clear, we will act in the national interest.
"We want to do what's right for the whole of the UK and bring stability to the government of the United Kingdom."
Some Tories, including the party's Scottish leader Ruth Davidson, are unhappy about a deal with the DUP because of the party's opposition to gay marriage and abortion.
In an apparent criticism of the move, Ms Davidson tweeted a link to a speech she made in Belfast in favour of marriage equality.
Later, the Scottish Tory leader said she had received "categoric assurances" from Mrs May over LGBTI rights.
"I was fairly straightforward with her (Mrs May) and I told her that there were a number of things that count to me more than the party," she said.
"One of them is country, one of the others is LGBTI rights.
"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 UK, in Great Britain, and that we would use any influence that we had to advance LGBTI rights in Northern Ireland."
Asked about the DUP's stance on LGBTI rights, British Defence Secretary Michael Fallon said the Conservatives "do not share their views and we do not have to".
"They are going to back us on the big issues," he told BBC's Andrew Marr.