Speaking in 10 Downing Street a day after the humiliating rejection of her Brexit plans at the EU summit in Salzburg, the Prime Minister recognised that negotiations had reached an "impasse".
But she dismissed EU suggestions that the onus is on Britain to shift its stance, insisting that the ball is now in the European Union's court.
Mrs May said she was ready to come forward with new ideas on unblocking the disagreement over future arrangements at the Irish border.
But, in apparent reference to European Council President Donald Tusk's assertion that her Chequers plan "will not work", she said: "At this late stage in the negotiations, it is not acceptable to simply reject the other side's proposals without a detailed explanation and new proposals.
"So we now need to hear from the European Union what the real issues are and what their proposals are so we can discuss them.
"Until we do, we can't make progress."
Mrs May added: "No-one wants a good deal more than me, but the European Union should be clear - I will not overturn the result of the referendum, nor will I break up my country.
"We need serious engagement on resolving the two big problems in the negotiations and we stand ready."