Andrew Wilson, author of the party’s Growth Commission report, said the fact that a majority of those who were born north of the Border voted for Yes in 2014 counted for little if most voters who had chosen to live in the country rejected it.
The former SNP MSP said Yes campaigners must stress that independence was “not a rejection of shared endeavour” between Scotland and other nations in the UK.
Mr Wilson added that voters from the rest of the UK living in Scotland would not be convinced to back an IndyRef2 if campaigners played “hardball”.
But the Tories said there was no demand among voters for a second referendum - regardless of where they were born.
“Tellingly, 72% of people born in the rest of the UK voted against independence,” Mr Wilson wrote in a column for The National. “Their concerns and those of their family and friends in the rest of the UK clearly weighed heavily and were not adequately addressed by the Yes side.
“Lessons must be learned there too. They represent around half a million votes, including more than 460,000 from England alone.
“A further half a million or so come from the everywhere else in the world, including around 300,000 EU nationals.”
Mr Wilson continued: “For those from the rest of the UK, though, what are we saying? What is our tone?
“First and foremost, it is not a rejection of 300 years of shared endeavour. It is not a severing of our economic, social, family or cultural ties - they will maintain and flourish. It is a political choice about how we are governed.”
Sharing the column, Nicola Sturgeon said it was about “how we learn from the grave errors of the Brexiteers, build an inclusive case for independence and value the bonds of friendship that will always endure across our islands”.
Scottish Conservative chief whip Maurice Golden MSP said: “Andrew Wilson will find whether you were born in Scotland or outside of it the opinion is the same – there is no demand for IndyRef2.
“We voted on Scottish independence in 2014 and it was a resounding no, it’s time that he respected that result.
“What people in Scotland now want is to move on from this debate and to have a Scottish Government that prioritises fixing our public services.”