The New York City mayor, Michael Bloomberg, said on Friday that public housing tenants should be fingerprinted, as a way of keeping criminals out of their buildings.

Bloomberg's comments, during a weekly radio appearance, appeared offhanded, and the city is not working on a program that would have building doors only open by a resident's fingerprinting. But the comments immediately drew criticism from several of the candidates who are battling to replace him at the end of his third and final term, in November.

The comment came just days after a court deemed a key Bloomberg public safety policy – the so-called "stop-and-frisk" policy – to be unconstitutional, because it unfairly targets minorities. Bloomberg was musing on WOR Radio that the court decision to limit the tactic may make it more difficult for police officers to protect New York City Housing Authority buildings. The police tactic – which allows officers to stop people deemed acting suspiciously – has been one of Bloomberg's most controversial policies.

As his 12-year tenure nears its end, Bloomberg has touted New York's falling crime rate as key accomplishment. The mayor, a billionaire and political independent, argues that stop-and-frisk has been critical to keeping New Yorkers safe. Critics say it unfairly discriminates against blacks and Latinos, the same groups that make up the bulk of public housing residents.

Within an hour of Bloomberg's radio appearance, the mayoral hopeful Bill Thompson derided the fingerprinting idea as "disrespectful" and "disgraceful." "Just like stop-and-frisk, this is another direct act of treating minorities like criminals," said Thompson, a former city comptroller, in a statement. "Mayor Bloomberg wants to make New Yorkers feel like prisoners in their own homes."

The public advocate Bill de Blasio, who is one of the front-runners in the mayoral race, called Bloomberg "out of touch" and urged the mayor to instead install security cameras within such public buildings, which house more than 400,000 people.

Bloomberg's spokesman later explained that the city is planning to install electronic key pads and key card locks on buildings, to improve security. He also noted that fingerprint-scan technology is becoming more common and is expected to be coming to smartphones.

On Friday, Bloomberg's government took the first step in challenging a federal judge's ruling imposing reforms on the stop-and-frisk strategy, filing a notice of appeal US District Court in Manhattan. Lawyers no have about three months to file the formal brief.

In her lengthy ruling on Monday, US district judge Shira Scheindlin ordered changes to officer training, discipline and supervision and appointed an outside monitor to supervise and come up with specifics on how the changes will work. She also has ordered changes to a police patrol program inside private buildings.