"What we have called for is a meaningful vote in parliament and that is the one area I think parliament has asserted itself in the vote before Christmas", he said.
Mr Sturgeon lashed out at the Labour leader on Twitter, arguing he was misleading people by arguing Brexit meant leaving the single market.
But when asked about Labour's stance could change in the future Mr Corbyn failed to deliver a clear response.
"But, at the moment, and as things now stand, we proceed in good faith, we do as we are instructed and we are leaving the European Union".
"The Single Market is dependent of membership of the European Union".
"At the moment... We proceed in good faith". She suffered a major voter backlash a year ago against her demand for a second independence referendum.
Within hours, Mr Farage appeared to row back, insisting he didn't want a second referendum and was merely trying to galvanise Leave campaigners to the inevitably of one. "We are leaving the European Union".
Talks of a second Brexit referendum were reignited when pro-Brexit politician Nigel Farage suggested a new vote could "silence" Remainers.
Among Labour voters 64% are in favour of a second referendum with 31% against.
Shadow Brexit secretary Sir Keir Starmer yesterday tried to play down divisions in Labour on remaining in the single market after European Union withdrawal.
"This amendment would not keep the United Kingdom in the single market and customs union, nor does it intend to deal with the serious flaws in this Bill", they said.
And she admitted that it was a "deep balancing act" to please both Labour voters who backed Brexit, and Labour members who want to stay in the EU.
Deputy Tory Party Chairman James Cleverly said today: "Every step of the way Labour are trying to frustrate the Brexit process rather than make a success of it".
The First Minister called on the Labour leader to get off the fence on the key issue, claiming there would be a Commons majority for staying in the single market if he threw his weight behind the plan.
If the Labour party announced tomorrow that we would keep Britain in the single market and customs union, it would be a game-changing moment in British politics.