"It's bizarre and so typically German to be arguing about the word Nafri instead of saying, 'fortunately there were no problems'," said Thomas Jaeger, a political scientist at Cologne University.
He said the row was "grist to the mill" of the anti-immigrant Alternative for Germany (AfD) party as it prepares for an election in May in North Rhine-Westphalia, the state that includes Cologne, and for a federal election in September.
"Police are being accused of racial profiling. What are they supposed to do? Screen all young women or grannies?" Jaeger said.
Racial profiling is not legal in Germany, but police have powers to screen anyone seen as a potential security threat. Security and immigration are both key issues as Chancellor Angela Merkel prepares to run for a fourth term, facing intense pressure for letting in more than a million migrants in the past two years.
A failed asylum seeker killed 12 people by ploughing a truck through a crowded Berlin Christmas market last month, emboldening critics who argue that the mass influx from countries such as Syria, Iraq and Afghanistan is exposing the country to terrorism.
Last year's Cologne sex attacks helped revitalise the AfD, which scored a series of electoral successes last year and beat Merkel's conservatives into third place in one state.
Ahead of the May 14 state vote in North Rhine-Westphalia, Germany's most populous state, the anti-immigrant party is polling over 10 per cent. It also threatens to erode Merkel's support in the national election.
AfD leader Frauke Petry weighed into the latest controversy with a sarcastic tweet, saying: "Nafris were probably on the way to join the church choir."
The German Interior Ministry said "Nafri" is not a term it uses and Cologne police chief Juergen Mathies said it was "unfortunate" that a term employed internally had been used in public. The police union said it was simply an acronym and not racist.
A Forsa opinion poll for RTL TV found 79 per cent believed Cologne police acted appropriately on New Year's Eve.
