Ministers say no part of the UK will be treated differently in the Brexit talks as Labour branded their approach an “embarrassment”.
No agreement has been reached with the EU after a DUP backlash against proposals for the Irish border.
Brexit Secretary David Davis told MPs the government was close to concluding the first phase of talks.
DUP leader Arlene Foster said the text of the deal was a “big shock” and “it was not going to be acceptable.”
She told the Republic of Ireland national broadcaster RTÉ that her party only saw the text on Monday morning, despite asking to see it for five weeks.
Theresa May, speaking as she welcomed Spanish Prime Minister Mariano Rajoy to Downing Street, said talks with the EU had ” made a lot of progress”.
“There are still a couple of issues we need to work on. But we’ll be reconvening in Brussels later this week as we look ahead to the December European Council,” she said.
Mrs Foster was invited to hold talks with Mrs May in London on Tuesday, but the party’s Westminster leader met the government’s chief whip instead.
The meeting lasted for several hours, but sources suggested to the BBC’s political editor Laura Kuenssberg that there was not much sign of a breakthrough yet, with a DUP insider saying the deal needed “radical surgery”, rather than a few word changes.
A phone call between Mrs May and Mrs Foster had then been expected this evening, but sources added that it would not go ahead, suggesting it had never been arranged.
The UK is due to leave the EU in March 2019 and Mrs May is under pressure to reach agreement on the Northern Ireland border so negotiations can move forward.
The prime minister needs the support of the DUP – the Democratic Unionist Party – which is Northern Ireland’s largest party and has 10 MPs at Westminster, because she does not have a majority to win votes in the House of Commons.
Responding to an urgent question from Labour in the Commons on Tuesday, Mr Davis defended the controversial proposal for “regulatory alignment” between Northern Ireland and the Republic of Ireland – intended to avoid the need for border checks after Brexit – saying this would…