"We are at the point of progressing to the next stage," May told parliament, after Northern Ireland's Democratic Unionist Party (DUP) blocked a proposed agreement on the Irish border being discussed in Brussels on Monday.
"We will ensure that there is no hard border between Northern Ireland and the Republic of Ireland.
"We will do that while we respect the constitutional integrity of the United Kingdom and we will be able to do that while we respect the internal market of the United Kingdom," she said.
The party opposed the agreement because it said it wanted no "regulatory divergence" between Northern Ireland and the rest of Britain.
"Now we need to look at the text, make it clear what we cannot agree with and try to work through all of that," DUP leader Arlene Foster said on Tuesday.
The EU has said Britain must make "sufficient progress" in negotiations on the Irish border, the future status of expatriate citizens and a financial agreement to unlock negotiations on post-Brexit trade arrangements.
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