Mike Russell said if a compromise is found enabling a deal to pass, people across the UK should be given the chance to vote on it.
He said this referendum should include the option to remain in the EU.
Speaking on BBC Radio Scotland’s Good Morning Scotland programme, he said: “What I would want to see at this stage is either no Brexit - that’s rescinding, revoking the Article 50 process - or, at the very least, a referendum on the choices before us.
“And the choice has to include revoking Article 50 and stopping this, because it’s been the most enormous disaster, the most enormous, costly disaster.
Asked if a second referendum should still be held if a compromise is reached on Theresa May’s Brexit deal before the current deadline of October 31, Mr Russell replied: “Yes. People have the right to choose, they have the right to say they don’t wish to do this.
“Things have changed enormously over the last three years and we also know that the original referendum was deeply flawed.
“I hope the Labour Party is in this position too in its discussions with the UK Government, because I don’t think it could be conceived of now without giving people the chance to say what they thought.”
Asked if he would accept the result of a second referendum, after Scotland voted 62% to remain and 38% to leave in 2016, he said: “If we got to the situation where Scotland continued to vote to stay in the EU and was being taken out against its will, nothing would have changed, that’s quite clear.”
He added: “I would not accept a situation where Scotland was taken out against her will, that would be impossible to do.”