A second referendum would be divisive but a price worth paying to prevent the "catastrophic damage" of a no-deal Brexit, Greater Manchester's mayor has said.
Andy Burnham said he would support a fresh vote only as a "last resort" to prevent the UK leaving the European Union with no agreement.
He said it could "widen" divisions and even "create social unrest".
The government said it was "confident of a mutually advantageous deal".
Speaking at Westminster, Mr Burnham argued if Parliament was heading towards a no-deal Brexit then the EU should be asked to postpone the March 2019 departure deadline to allow further negotiations.
If that fails and a deal acceptable to Parliament cannot be agreed between the UK and Brussels, a second referendum should be held, the former Labour cabinet minister said.
"I have to think seriously about what a second vote would mean on the streets of Greater Manchester," he said.
"If we thought the first was bad, the second would be a whole lot worse.
"It won't heal divisions but widen them, it would be angrier, create social unrest and open up a massive opportunity for the populist far right in a way we are seeing elsewhere in Europe and the USA."
Mr Burnham said the alt-right could be pushing the no-deal agenda "to exploit splits in British society".
'Further erode trust'
However, he also said he was not supporting the People's Vote campaign for a referendum, and only advocated a second vote if the alternative was leaving with no deal.
He continued: "A second vote would further erode trust in Parliament and politicians, but that price is worth paying to stop the catastrophic damage to jobs that would come with a no-deal Brexit."
Mr Burnham, who is campaigning for extra powers to be given to the devolved regions and cities, said the 2016 Brexit referendum result was as much an "instruction for Westminster to review its relationship with the rest of England" as a message to Brussels.
"If the phrase 'take back control' is to mean anything, it must mean substantial devolution of power and resources out of Westminster to all of the English regions," he said.
A spokesman for the Department for Exiting the European Union said: "As a result of the significant progress made in negotiations, we remain confident we will agree a mutually advantageous deal with the EU."