"Our absolute focus should be on working to get a deal and leaving on March 29".
But she said such a move would ignore the wishes of millions of Labour voters who voted Leave at the 2016 referendum.
With just over a month until Britain is due to leave the bloc, Prime Minister Theresa May is seeking changes to her exit deal in order to break an impasse in parliament.
Since Parliament overwhelmingly rejected her withdrawal deal last month, May has appealed to reluctant European leaders to give her a legally binding assurance that Britain won't be chained to EU customs and trade regulations forever, in an effort to keep the border between Northern Ireland and the Irish Republic open and invisible.
The deadlock of a parliament which can't agree to support anything - not a deal, not no deal, not a second referendum - can't continue forever.
It follows days of speculation that Labour might be moving towards backing a public vote.
Labour is not yet making clear what its proposed referendum would be on.
Cabinet ministers have told Theresa May she must use any delay to Brexit to face down the Eurosceptic wing of the party and forge a consensus in parliament, as the prime minister finally conceded to offer a vote on extending article 50.
The mechanism, known as the backstop, is a safeguard that would keep the United Kingdom in a customs union with the EU to remove the need for checks along the Irish border until a permanent new trading relationship is in place.
May wants to change the deal to reassure British lawmakers that the backstop would only apply temporarily. Brexit has proved to be such a divisive issue that both mainstream parties have suffered defections.
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The EU has been watching with growing concern the possibility that Britain will crash out of the bloc without a deal, risking chaos on both sides of the Channel. The Bank of England has warned that the British economy could shrink by 8% in the months after a disorderly Brexit.
If her plans are backed by MPs on Wednesday, Mrs May will return to the Commons by March 12 for a further "meaningful vote".
If that fails, MPs will be offered two separate votes on the following days - one on a no-deal Brexit and, if that is defeated, the other on requesting an extension to the two-year Article 50 negotiation process to delay European Union withdrawal beyond March 29.
The 2016 referendum, in which 17.4 million voters backed leaving and 16.1 million backed staying, showed a country divided about much more than the European Union, and has fuelled soul-searching about everything from secession and immigration to capitalism and modern British identity.
"I don't see how businesses can plan, I don't see how public services can plan and I think it's just deeply damaging", Cooper told the BBC.
The EU's Tusk warned that the chances of a withdrawal agreement being concluded in time are receding, and that sticking by the planned Brexit date would be too risky.
After her statement, Jeremy Corbyn, the leader of the opposition Labour Party, told the House of Commons: "I've lost count of the number of times the Prime Minister has come to this house to explain a further delay".
That alone means that May has failed in her primary responsibility following the 2017 General Election - when she failed to deliver a majority - which was to deliver Brexit.
May said that if such an extension were triggered, it would likely be granted only once and that the time would be "short and limited".
"She promises a short extension but for what?"