DUP leader Arlene Foster, who was asked to resign in the wake of a heating incentive scandal that cost the government hundreds of thousands of pounds, said on Twitter that discussions are "going well" and that there will be an agreement of sorts.
"The idea that the United Kingdom led by this prime minister and this government can just blunder into negotiations starting one week today, I just don't think it's a credible proposition", she told reporters in London.
A DUP spokesman told AFP there had been a break in the talks due to parliamentary business. Now Sinn Fein has indicated that it could end its century-long boycott of the British Parliament in order to block the DUP-Tory alliance and get a deal with Labour for a referendum on Irish unity.
May is under pressure to take on a more cross-party approach to Brexit talks.
She told a meeting of backbenchers that she had got the party into "this mess" by calling the snap election and now "I'll get us out of it".
Before the election, May proposed a clean break from the European Union, involving withdrawal from Europe's single market, limits on immigration and a bespoke customs deal with the EU.
Former Tory Prime Minister John Major, who has raised concerns about the potential alliance, warned the more extreme elements in both Catholic and Protestant communities could see an opportunity to re-enter the fray.
May made clear the Brexit negotiations would begin next despite uncertainty.
The possibility of an additional year in the Brexit negotiations under Article 50 of the Lisbon treaty illustrates the intense frustration in Europe's capital city.
Among these was whether Britain's position would "be the same as in the letter of March 29" when May triggered the two-year Brexit countdown.
"It's passing quicker than anyone believes".
"We would restore faith in politics if we could show that this parliament can at least function in presenting a view in the national interest which would command a majority on a cross-party basis", said veteran pro-European Conservative lawmaker Ken Clarke.
The talks are being closely watched in European capitals as they could delay the expected start of Brexit negotiations next week.
Mr Barnier held "talks about talks" in Brussels with Mrs May's Brexit adviser Olly Robbins and Britain's ambassador to the EU, Tim Barrow, on Monday but they failed to agree on a date for the negotiations to begin.
They would not form a coalition.
The DUP has blocked all progress on equal marriage in Northern Ireland, and supports the introduction of a "conscience clause" to protect people who discriminate against LGBT people.
The Northern Irish party's stance on equality has been under scrutiny this week, as numerous MPs that Theresa May will be relying on harbour actively homophobic views.
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