He argued the party’s commitment to the European Union has been “compromised” amid growing speculation the SNP is preparing to announce a second referendum within weeks.
First Minister Nicola Sturgeon has previously said a second independence ballot was “highly likely” following the Brexit vote.
It has been reported that her party is preparing to drop full membership of the EU as a key part of its independence case, and instead push for a Norway-style model which would allow Scotland to remain in the single market via the European Free Trade Area and European Economic Agreement.
During a speech at the David Hume Institute in Edinburgh, Mr Rennie said the move is an attempt to appease independence supporters who voted to leave the EU.
The Lib Dems are pursuing a Brexit deal referendum, which they say would allow voters the chance to change their minds if they do not like the arrangements agreed between the EU and the UK Government at the end of their negotiations.
“Independence is not the economic or the emotional answer to Brexit,” Mr Rennie said.
“I will continue to stand for Scotland in the UK as much as the UK in the EU. I will not compromise on deep rooted principles of internationalism, openness and liberalism.
“The Scottish National Party’s commitment to the EU has been compromised.
“You haven’t heard any senior nationalist say ‘the only way to keep Scotland in the EU is to have independence’.
“They used to say that all the time. Now they don’t. They now say that their dissatisfaction with the UK Government ‘transcends the issue of Europe’.
“We, perhaps, should not be surprised as one third of their supporters favoured Brexit.
“I meet them every week on the doorsteps. Brexit supporters who backed independence in 2014 but are opposed now because of the independence in Europe policy.
“Desperate to keep the significant branch of Brexiteers in their own party in line they are prepared to sell out Europe to get their dream of independence.
“So the risk of their proposal is that it leaves Scotland outside the UK and outside the EU. What a disaster that would be.
“It would only be right for the British people to have the final say on whatever deal is agreed by the Conservative Government with the EU.
“A Brexit deal referendum would be the right and democratic thing to do.
“When they look back at this time, our grandchildren will be perplexed that we did not take our time and ask ourselves the question if we really wanted this.”