The SNP Brexit Minister said it would be "very foolish to guess" how much Scotland would have to cough up but asked about the figure claimed it would be "a small price to pay".
His comments came as he was grilled by MPs over Nicola Sturgeon's demand for a Norway-style deal allowing the country to remain in the trading zone even when the UK leaves.
Scottish Tory deputy leader Jackson Carlaw said Mr Russell "was all at sea" adding: "The cat is out of the bag: the SNP would sign a blank cheque in order to leave our own domestic market and join the EEA.
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Mike Russell was accused of writing ‘a blank cheque’ to stay in the EU's single market
“Everyone knows why – it's because they are willing to pay any price to achieve their goal of splitting the UK and winning independence."
The SNP would sign a blank cheque in order to leave our own domestic market and join the EEA
Jackson Carlaw – Scottish Tory deputy leader
The First Minister published a blueprint before Christmas that said Scotland could join the European Free Trade Association (Efta) and the European Economic Area (EEA) to gain full access.
But existing members are required to make financial contributions to the bloc, which the Scottish Government said would be "a matter for negotiation".
It did however estimate the UK would have to pay around £3.3billion a year to be an EFTA member, and suggested Scotland's cash could be found from a pro-rata share of current EU contributions.
Russell also faced a barrage of criticism from Tory MP and leading Leave campaigner Michael Gove
Mr Russell appeared confused on the issue as he was questioned at the Common's exiting the European Union committee.
He also faced a barrage of criticism from Tory MP and leading Leave campaigner Michael Gove as he struggled to answer questions over how financial services, banking, and medical research would be regulated under a "differentiated" agreement.
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During heated clashes, Mr Gove asked: "So Scots would have to pay £3.3 billion to stay in the single market?"
Mr Russell replied: "If that was the price to stay in the single market it would strike me as a small price to pay for the lack of dislocation which you and your colleagues are forcing upon this country."
Russell was grilled by MPs over Nicola Sturgeon's demand for a Norway-style deal
Earlier, challenged over how Brussels rules would affect Scottish firms he said it was "a matter for detailed discussion".
Questioned over whether the financial services sector would be overseen by an EU regulator Mr Russell said: "I'm not looking at my smartphone, unlike you, so I can't look at who it is but I'm quite sure I could, were I to use Google."
He added: "I’m quite prepared to provide a list of things I do not know, it will be a very long list, there are many things I do not know
"What I do know is that we have made a series of interesting and detailed proposals which we would like to negotiate with the UK Government."
Later Mr Russell accepted the £3.3billion figure referred to the UK as a whole after other committee members corrected the record.
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Continued cooperation with the EU to tackle terrorism and international crime.
Tory MP Peter Lilley cited Remain campaign estimates that Norway pays about £96 per head for access to the single market.
This could see Scotland facing a £515 million bill – though the Scottish Government previously suggested a UK net contribution of around £52 per head.
Repeating warnings of dire economic consequences of a hard Brexit, Mr Russell added: "Actually the cost of contributing to the single market would seem a bit of a bargain compared to the cost Scotland would have to pay."
The clashes came ahead of another meeting of the Joint Ministerial Committee (JMC) where the Scottish Government's Brexit proposals are being considered.
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