"I don't quite understand why she would keep saying, "join the single market" when leaving the European Union means you leave the single market", the Labour leader said in response to Ms Sturgeon's appeal.
Jeremy Corbyn rebuffed a call from Nicola Sturgeon for Labour to back the UK's continued membership of the European single market, saying Brexit meant the United Kingdom had to quit the EU trading bloc.
But less than half an hour later Mr Corbyn rejected her demand, saying he did not "understand" why she was focusing on the single market when Brexit meant leaving it.
But he said the existing arrangements needed improvement.
In an interview with The Observer today, the former Ukip leader said he was anxious Brexiteers could "lose the historic victory" they won in 2016 as "The Remain side are making all the running".
But when asked about Labour's stance could change in the future Mr Corbyn failed to deliver a clear response.
"We are not supporting or calling for a second referendum", he said. "What we have called for is a meaningful vote in parliament".
But Corbyn said: "We are not supporting or calling for a second referendum". Is that what we have said to the European Union in opposition? Yes.
Niumatalolo no longer a candidate for UA coaching job
Before taking over in 2007, Niumatalolo served as the assistant head coach and offensive line coach from 2002 up until that point. Niumatalolo has gone 84-48 as Navy's head coach, and has been the subject of interest from bigger schools before.
"There is no reason why the United Kingdom, if we leave, should not have that kind of relationship".
"We have said that we must respect the result of the referendum which means that we have to leave, but we have to look after the economy which, in my view, means that we don't go very far".
Media captionBamboozled by Brexit?
Deputy Tory party chairman James Cleverly said the comments showed that Labour was trying to frustrate Brexit.
Pro-Remain Labour Chuka Umunna also questioned the statement, pointing out countries like Norway and Iceland maintained access to the single market despite being outside the European Union. The SNP, Liberal Democrats, Plaid Cymru and Greens have joined forces to back an amendment to the EU (Withdrawal) Bill when it returns to the Commons this week.
Labour's Brexit policy is now the single biggest barrier to Britain remaining in the European Union single market, the Ilford North MP, Wes Streeting, will claim on Saturday.
The shadow Brexit secretary, Keir Starmer, has said permanent membership of a customs union with the EU27 could be a "viable" longterm option and should be kept on the table.
He told ITV's Peston on Sunday programme: "Do we have a trading relationship with Europe which is tariff free, which is based on access to that market, and access of Europe to our market? Yes".