British Prime Minister Theresa May | Jack Taylor/AFP via Getty Images Theresa May: No-deal Brexit preferable to EU offer UK prime minister says no deal would be preferable to a deal that leads to the breakup of the UK.

NEW YORK — No Brexit deal would be preferable to European Union proposals that break up the United Kingdom, Theresa May said Tuesday en route to the U.N. General Assembly in New York.

Speaking to journalists on the flight, the prime minister reiterated her claim that no deal is better than a “bad deal,” citing the breakup of the United Kingdom as an example of a bad deal.

“What we have put on the table is a good deal, it’s a deal which retains the union of the United Kingdom, our constitutional integrity, it’s a deal that provides for no hard border between Ireland and Northern Ireland, protects jobs and enables us to have a good trading relationship with Europe and also the rest of the world,” she said.

The prime minister’s official spokesman told reporters on Monday that the EU’s offer of a Canada-style free-trade agreement (FTA) would only apply to Great Britain, not Northern Ireland.

“Given a standard free-trade agreement could not prevent a hard border between Northern Ireland and Ireland, the EU’s position is that their proposed Northern Ireland protocol would come into affect, so the FTA would only apply to the Great Britain/EU relationship with Northern Ireland effectively remaining in parts of the single market and the customs union,” he said.

May accused Labour of positioning itself to oppose any deal “regardless how good it is for the U.K.”

May was asked if no deal is better than the so-called Canada plus model, which is being advocated by some Brexiteers including David Davis and Boris Johnson, the former Brexit and foreign secretaries. They dislike her Brexit plan agreed by ministers in July at her Chequers country residence that would mean the U.K. abiding by a common rule book with the European Union in some areas.

EU leaders have also rejected the Chequers plan because it seeks to divide the four freedoms of the EU single market. At an acrimonious EU summit last week in Salzburg, Austria, European Council President Donald Tusk said that May's plan "will not work."

“It must be clear that there are some issues where we are not ready to compromise, first of all this is our four fundamental freedoms and single market, this is why we remain skeptical and critical when it comes to this part of the Chequers proposal,” he said. On Friday last week he added that the U.K. had been aware of Brussels' objections for weeks.

That comment was prompted by a defiant statement from May in Downing Street in which she demanded "respect" for the U.K. The prime minister doubled down on that position Tuesday. "I have always said no deal is better than a bad deal. I think a bad deal would be for example a deal that broke up the United Kingdom," said May. A no-deal would very probably lead to a hard border in Northern Ireland.

May said she believes the U.K. could get a good deal that she would take back to parliament to give MPs a clear choice. “They will have to recognize, looking at their vote, that what we are doing is delivering on the vote of the British people in the referendum,” she said.

May accused Labour of positioning itself to oppose any deal “regardless how good it is for the U.K.”

“They will accept any deal the EU gives regardless of how bad it is for the U.K. That is not in the national interest; what we are doing is in the national interest,” she said.