The head of the pro-UK Better Together group claimed on Tuesday that Jean-Claude Juncker’s remark that the 28-member bloc needed “a break from enlargement” for five years showed an independent Scotland would be kept out of the EU.
Mr Juncker’s spokeswoman has since said he was not referring to Scotland.
She told The Scotsman: “At no point is Scotland mentioned, as this is an entirely separate issue.”
Ms Sturgeon, in a letter to Mr Darling, attacked what she said was the “dishonesty” of the Better Together campaign.
She called on Mr Darling to apologise and to remove online content from the No campaign website that said “Juncker Ends Salmond’s European Dream”.
In the letter, Ms Sturgeon said: “Better Together’s assertions about what the new president of the European Commission has said in terms of European Union enlargement are demonstrably false. Your campaign deliberately misinterpreted those remarks by issuing a statement claiming that Mr Juncker had suggested an independent Scotland will not continue in EU membership.
“That claim – as Mr Juncker’s office have now made completely clear – was totally without foundation.”
But a spokesman for Mr Darling dismissed Ms Sturgeon’s claims and maintained Mr Juncker’s comments suggested Scotland would have to apply to join the EU as a new member state.
He said: “President Juncker’s comments lay bare the full extent of the problems we would face if we left the UK. The countries who have already started the application process to join the EU face a five-year wait. As President Juncker has made perfectly clear previously, if we leave the UK, we would then have to start the application process to join.”
Pro-Union campaigners have said the commission chief’s remarks show a Yes vote in the independence referendum will also be a vote to leave the EU.
The SNP has claimed an independent Scotland would automatically inherit EU membership due to its former status as part of the UK, and would only have to renegotiate its membership terms as a new state. This Nationalists say this could be achieved by March 2016, the date they have earmarked for independence if there is a Yes vote.
The SNP states that, unlike candidate countries in the Balkans, Scotland’s laws and regulations are already “100 per cent compatible” with the EU’s.
The issue is crucial as Scotland’s participation in international tie-ups such as the World Trade Organisation would have to be renegotiated if it exited the EU or was outside for a long period, meaning a significant impact on jobs and growth.