The SDLP's Jimmy Carr, who represents the Shantallow area on Derry City Council, made the comments about Sinn Féin's Eric McGinley on Facebook.
The row developed after the SDLP backed awarding a £200,000 grant to the Bogside Artists, for the restoration of their famous murals, but were blocked by Sinn Féin who backed a grant of £45,000.
"The history of derry according to Sinn Fein. And what makes it all the more sickening is the shinner who put forward the proposal to block is a Scotch man!" Mr Carr later posted on Facebook.
He is representing Derry and he is not from this city. I genuinely don't understand a word of what he says.
Jimmy Carr, SDLP
In a statement, Sinn Féin's group leader on Derry City Council, Paul Fleming, said that he thought people would be shocked by the comments.
"What is this saying to all nationalities who wish to visit Derry, work here, set up home here - or indeed take on the role of an elected representative?" he added.
While Mr Carr initially insisted that he was standing by the comments and didn't intend to withdraw them, the SDLP councillor has since apologised and expressed regret for not retracting the remarks.
"As well as offering my apology to Cllr McGinley, I also want to apologise to all my party colleagues and members for expressing myself in such terms that failed to represent the SDLP's ethic of inclusion and respect for diversity," he said.
"I respect the valuable contribution that many people who are originally from outside Derry make in so many ways to the life of this city.
"I should not have allowed any frustration in the Council Chamber or in the media to come over as prejudiced or insensitive in any way."
Mr Carr added: "I hope that Cllr McGinley, my own party and the Derry public whom I am proud to serve will accept this reflective retraction as a truer measure of my nature than the rash words or defensive outbursts which caused the offence which I recognise and want to repair."