Mr Corbyn says the party will take this position to stop "no deal or a damaging Tory Brexit".
But he does not say what he would do if he won a general election and was placed in charge of the Brexit process.
Some senior members of his team want him to take a pro-Remain stance in all circumstances.
In an interview with the BBC's John Pienaar, Mr Corbyn said Labour was now the "party of choice" when it came to Brexit.
He said he had done "what I think a leader should do... an awful lot of listening" - to party members, unions and the wider Labour movement - before coming to a revised position.
He said he would "make a case" to Parliament in September to get another referendum and in the meantime, Labour will "do everything we can to take no deal off the table or stop a damaging deal of the sort Hunt or Johnson propose".
Asked if he had changed his position because of pressure from colleagues, Mr Corbyn said: "Not a bit of it. I've been listening and I've enjoyed it."
Mr Corbyn said he could not say what Labour's position would be at a general election, but would decide it "very quickly", depending on the circumstances at the time, whenever one was called.
In a letter to members, he said Labour continued to believe the "compromise plan" set out for Brexit during cross-party talks with the government earlier this year was a "sensible alternative that could bring the country together". [...]