The EU's chief Brexit negotiator Michel Barnier has reiterated the importance of striking a deal with the United Kingdom that stops the return of a hard border between Northern Ireland and the Republic of Ireland.
Speaking after the meeting, DUP leader Arlene Foster said: "We want to see a Brexit that works for everybody, not just in Northern Ireland from my perspective, but in the Republic of Ireland as well, so it is about a sensible Brexit".
Despite the concerns, the same DUP sources said later that a substantive deal to support a Conservative administration could still finalised by Thursday, before May is due to be in Brussels for a meeting of the European Union council.
The news is a significant blow to the authority of Mrs May who said hours after the election that she would seek a deal with the DUP's 10 Westminster MPs after she failed to win a majority of MPs in the House of Commons.More news: Amnesty urges donors to give more to South Sudan refugees
Speaking outside Downing Street the day after the poll, the PM said that she would "continue to work with our friends and allies in the Democratic Unionist Party" to ensure she was able to command a majority to get her legislation through.
After initial signs of progress, the Conservatives were forced to row back on a premature announcement that agreement had been reached, and talks have now dragged on for 11 days without reaching a conclusion.
It is thought that the DUP is pressing for more investment for Northern Ireland as part of the price of its support, and that it is also calling for the retention of the triple lock guarantee on pensions and universal winter fuel payments for older people.
Meanwhile, talks between NI's political parties began this week to restore power sharing.More news: Does Trump think Russia hacked the election? Spicer doesn't know
Indeed, it seems likely that the Conservative relationship with the DUP, having started in a fairly good place, has gotten worse in these weeks of direct talks.
"Theresa May has no mandate for the direction she is taking the country".
Prime Minister Theresa May will tomorrow push ahead with her post-election plans, despite failing to reach a deal guaranteeing her ability to govern.
An agreement appeared unlikely before Wednesday's Queen's Speech, denying Ms May the guaranteed Commons majority she was seeking when she sought the DUP's support.More news: City Celebrates Aboriginal Day June 21
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