"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 DUP, which has been propping up May's government ever since a general election in June in which she lost her parliamentary majority, has said it only saw a draft copy of the proposed deal on Monday.
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.
EU leaders have given May a deadline of the end of this week to resolve outstanding issues in order to draft an agenda in time for a crucial EU summit on December 14-15 and open this second phase of talks.
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