And Green Party co-leader Caroline Lucas said: "We urge the Labour leadership to join us in backing this crucial amendment - and show that they too are willing to put the national interest first".
He said: "Once again the very top of Labour, this time Jeremy Corbyn and Emily Thornberry, have failed to rule out a second referendum".
He told ITV's Peston on Sunday: "We are not supporting or calling for a second referendum".
It comes after shadow Brexit secretary Sir Kier Starmer told an audience at the Fabian Society conference in London that Labour would vote against any Brexit deal that did not contain the "exact same benefits" that the United Kingdom now enjoys through membership of the single market and customs union.
Mr Sturgeon lashed out at the Labour leader on Twitter, arguing he was misleading people by arguing Brexit meant leaving the single market.
"You have to make a special relationship with the European Union".
A spokesman for the Department for Exiting the European Union said: "We respect the four freedoms of the EU and that is why, as we leave the EU, we are leaving the single market and customs union".
"At the moment... We proceed in good faith". I understand the views of Labour supporters.
He said he hated the term "second referendum".
Foreign Secretary Boris Johnson
One challenged him and said "let us leave".
Labour leader Jeremy Corbyn has stopped short of ruling out a second European Union referendum when the Brexit terms are known.
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". However the survey said only 18% of Tory voters want a second poll and 79% were against.
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. 87% of party members want to stay in the single market, a recent poll showed.
He said if the Labour leadership committed to staying in the trading arrangement it would be a "game-changing moment" in British politics as it would command a majority of cross-party MPs.
The comments came after Labour MP Wes Streeting said the party was now the "single biggest barrier" to Britain remaining in the single market.
Lib Dem, SNP, Plaid Cymru and Green Party leaders are tabling the amendment.
Single market membership after Brexit has become a divisive issue within Labour, with members struggling to reach a common party line on the matter.
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