An EU proposal for the Northern Ireland border threatens the "constitutional integrity" of the United Kingdom, Theresa May has said.
The EU's draft legal agreement proposes a "common regulatory area" after Brexit on the island of Ireland - in effect keeping Northern Ireland in a customs union - if no other solution is found.
Mrs May said "no UK prime minister could ever agree" to this.
The EU says the "backstop" option is not intended to "provoke" the UK.
Unveiling the draft agreement, EU chief negotiator Michel Barnier called on the UK to come up with alternatives.
He said the text was "no surprise" and was just a legally-worded assessment of what had been agreed so far.
Mr Barnier said the document contained "concrete and realistic solutions" in relation to the question of how to avoid a hard border once the UK leaves the EU's customs union.
Other options - a UK-EU deal that means checks are not needed and technological solutions - will also be explored.
Speaking at Prime Minister's Questions, Mrs May said she would be making her opposition to the "backstop" option "crystal clear" to the EU commission.
"The draft legal text the commission have published would, if implemented, undermine the UK common market and threaten the constitutional integrity of the UK by creating a customs and regulatory border down the Irish Sea, and no UK prime minster could ever agree to it," she said.
The prime minister was responding to a question from David Simpson of the Democratic Unionist Party, which gives the government the Commons support it needs to win key votes in the House of Commons.
Earlier the DUP's Westminster leader Nigel Dodds said his reaction to the publication was one of "amazement" that the EU thought it "could possibly fly with either us or the British government".
"We did not leave the European Union to oversee the breakup of the United Kingdom," he told the BBC, adding that it would be "catastrophic" for Northern Ireland to be "cut off" from UK markets.
Conservative Brexiteers have also said it is "completely unacceptable" and would effectively annex Northern Ireland.
There is also opposition to any role for the European Court of Justice after Brexit - the EU is proposing that disputes over the Brexit agreement in future years be settled by a "joint committee" which can refer to the EU's court for a binding decision.
Downing Street said that overall the negotiations were "progressing well", adding that "it would be surprising at this point if we did agree on everything".
According to the draft text, the "backstop" would involve an "area without internal borders in which the free movement of goods is ensured", covering customs, VAT, energy, agriculture, goods and other sectors.
"The territory of Northern Ireland... shall be considered to be part of the customs territory of the Union," it says.
The Irish government said this option was "very much a default and would only apply should it prove necessary".
Ireland's foreign affairs minister Simon Coveney said the publication was "another important step in the Brexit negotiations".
Labour says it would solve the Irish border question by entering into a new customs union with the EU, meaning checks are not needed as people and goods pass between Northern Ireland and the Republic.
Shadow Brexit Secretary Sir Kier Starmer said: "The EU-UK Government war of words needs to end.
"There can be absolutely no deviation from the solemn commitments made to Northern Ireland at the end of the first phase of Brexit negotiations. That means no hard border or any agreement that would undermine the Good Friday Agreement.
"Theresa May's failure to offer any viable solution to the border in Northern Ireland has come back to haunt her."