Stephen Brown, who is one of two SNP candidates standing in the Dalry and West Kilbride ward of North Ayrshire council, made the now deleted remarks on Sunday.
In an exchange with unionists on social media, Brown told one pro-Union account “Sadly agree … but maybe you’ll emigrate after #indyref2 as we will need the space for all the civic minded Europeans.”
Brown has since deleted his entire Twitter account.
The businessman, as treasurer of Citizens Advice Scotland, was once criticised for appearing to falsely claim that he was a Lord who was descended from royalty,
The SNP is looking to regain control of North Ayrshire Council after the previous administration led by Joan Sturgeon, mother of First Minister Nicola Sturgeon, stepped down.
The party was left as the second-largest midway through the term after an unsuccessful attempt by Sturgeon’s father Robin to win a by-election.
Contacted by the Scotsman, Brown initially said that he was responding to a ‘Nazi’ earlier in the exchange before claiming that he didn’t remember making the remark in question.
He said: “I set that account up as part of my council campaign, and I only lasted a few hours before I had to delete it due to all the hate I received. There was so much anti-nationalist abuse.
“I won’t make a comment on that remark one way or the other because I don’t remember making it – I have no specific comment to make.”
A spokesman for Scottish Labour said: “This is an unacceptable comment from an SNP council candidate and shows just how divisive nationalism can be.
“Kenneth Gibson will surely want to distance himself from Mr Brown.
“We know that SNP candidate selection has already been a disaster – with IRA sympathisers and convicted anti-English racists making it on to the SNP books.
“Meanwhile, Labour members across Scotland are out uniting communities and campaigning to protect local services from savage Nationalist cuts.
“Labour believes that together we’re stronger, which is why we will oppose a divisive second independence referendum.”