Ahead of a potential Democratic presidential run, former Mayor Michael R. Bloomberg of New York on Sunday reversed his longstanding support of the aggressive “stop-and-frisk” policing strategy that he pursued for a decade and that led to the disproportionate stopping of black and Latino people across the city.

“I was wrong,” Mr. Bloomberg declared. “And I am sorry.”

The speech, Mr. Bloomberg’s first since he re-emerged as a possible presidential candidate, was a remarkable concession by a 77-year-old billionaire not known for self-doubt: that a pillar of his 12-year mayoralty was a mistake that he now regrets. It was also, in some ways, a last word on an era of aggressive policing in New York City that began a generation ago under former Mayor Rudolph W. Giuliani — though the fallout on neighborhoods is still felt to this day.

Speaking before the congregation at the Christian Cultural Center, a black megachurch in Brooklyn, Mr. Bloomberg delivered his apology in the heart of one of the communities most affected by his policing policies, and at a location that nodded to the fact that should he decide to run for president, African-American voters would be a crucial Democratic constituency that he would need to win over.

Mr. Bloomberg’s policing record negatively impacted huge swaths of people of color across New York, so much so that his support for “stop and frisk” is seen as one of his biggest potential vulnerabilities in 2020. During his 12-year tenure, there were millions of street stops heavily targeting black and brown young men. Few Democrats have such an indelible record on race in a party where black voters helped determine the winners of the last two contested presidential primaries, Barack Obama in 2008 and Hillary Clinton in 2016.