“I was wrong, and I am sorry,” Mr. Bloomberg, 77, said of his longstanding and controversial support for “stop-and-frisk” policing, which allowed officers to detain someone for search and questioning.

Mr. Bloomberg’s abrupt reversal on stop-and-frisk — a policy that studies have shown disproportionately affected blacks and Latinos, and that a federal judge ruled unconstitutional in 2013 — drew criticism . And for Mr. Bloomberg, who declared his candidacy on Sunday morning, the issue of stop-and-frisk has already raised questions about how his mayoral record will be regarded by American voters.

Shane Goldmacher, my colleague on The Times’s Politics desk, called Mr. Bloomberg’s $30 million purchase of television ads this week — including $1.6 million worth in New York City — a sign that he is hoping to define himself as a strong leader.

Speaking by phone from Iowa — where Senator Elizabeth Warren of Massachusetts was campaigning, and had already accused Mr. Bloomberg of trying to buy the Democratic nomination — Mr. Goldmacher said Mr. Bloomberg’s time as mayor will be scrutinized if he gains in the polls.

“But for now,” he said, “most of his opponents would rather talk about him being rich.”

Mr. Goldmacher said he wasn’t surprised about Mr. Bloomberg’s stop-and-frisk reversal because “African-American voters have represented a decisive voting bloc in Democratic primaries.”