New York (CNN) -- Rather than celebrating Father's Day on Sunday afternoon, Horace Russell marched with several thousand people to take a stand against the New York Police Department's controversial "stop and frisk" policy.
"I feel it every single day, practically," said Russell, who works as a teacher in the Bronx. "I've been pulled over and pushed against fences, frisked, but have never been arrested."
Russell's story sounded familiar to many of Sunday's marchers, who want to see action from Mayor Michael Bloomberg, and Police Commissioner Ray Kelly -- either by abolishing or reforming stop-and-frisk.
Last year, nearly 685,000 people were stopped by officers in cases that ended with no meaningful charge, according to police department statistics. Of these, 87% were African-American or Latino, the police department says.
"They profile me because I'm a Rastafarian and I have dreadlocks, so therefore I get pulled over just for my looks," said Russell.
Sunday's silent march started at 110th Street and headed down Fifth Avenue, ending at 78th Street after passing Bloomberg's townhouse on 79th Street.
"I don't know a single black or Latino male who doesn't say he is basically afraid to be out on the streets," said the Rev. Stephen Phelps, a senior minister at the Riverside Church near West Harlem. He was one of a diverse group of faith leaders, and representatives of some 300 organizations , brought together by the Rev. Al Sharpton's National Action Network.
On Sunday morning, speaking at a Christian Cultural Center, Mayor Bloomberg attempted to preempt the demonstration's inevitable message: "I understand why some people want us to stop making stops," he said.
"Innocent people who are stopped can be treated disrespectfully. That is not acceptable... Police Commissioner Kelly and I both believe we can do a better job in this area -- and he's instituted a number of reforms to do that.
"We believe that when it comes to making stops -- to borrow a phrase from President Clinton -- the practice should be mended, not ended."
However, in official circles, there appears to be strong divergence in opinion.
"It's racial profiling of people who are almost all innocent of any wrongdoing," said New York City Comptroller John Liu, who was advocating abolition at the protest march. He said he would prefer "strategies of focused deterrents that we have seen in Atlanta, Chicago and Boston that actually reduce crime."
Jumaane Williams, a New York city councilman from Brooklyn, said Bloomberg and Kelly "have shown no leadership" on the stop-and-frisk issue. "Inherent in any police officer's ability to do their job is their ability to stop somebody they feel is reasonably suspicious. The current policy is not that -- it's stopping people because they are black or brown."
Williams added, "Whether you say end it or reform it, we have to end the way that policy currently exists."