“Redlining specifically targeted black and brown communities and has been part of all the ways in which systemic exclusion from wealth and income has hit communities of color,” said Rashad Robinson, president of the civil rights group Color of Change.

“The fact that he and his campaign would try to redefine this rather than talk about how they’re going to solve it speaks to not just a level of tone-deafness about this moment that we are in, but a really deep dismissal of the pain that has caused so many families and so many communities,” he said.

Mr. Bloomberg has sought to address the criticism over his record on race, which picked up this week after remarks he made in 2015 about stop-and-frisk resurfaced. In them, he said that “ninety-five percent of your murders — murderers and murder victims — fit one M.O.” Specifically, he said, they were “male, minorities, 16 to 25.”

In a statement on Tuesday, he apologized for “taking too long to understand the impact” that stop-and-frisk policing “had on Black and Latino communities.” His statement, which noted that he “inherited” the policing tactic before cutting it back, omitted the role he played in expanding stop-and-frisk, and ignored that the decline he cited was partly the result of litigation and political pressure.

At an African-American outreach event in Houston on Thursday, Mr. Bloomberg spoke at length about the policing policies he oversaw as mayor. He said he would have acted sooner to end stop-and-frisk had he understood the “pain it caused to young black and brown kids and to their families.”

“And for that I apologized,” he added, drawing applause and murmurs of approval from the audience of several hundred.

Mr. Loeser, the Bloomberg spokesman, said in his statement on Thursday, after the redlining comments emerged: “Because he knows how important it is to keep people in their homes, Mike attacked predatory lending as mayor and helped other cities craft innovative strategies to reduce evictions as a philanthropist. And Mike has detailed plans for how he will help a million more black families buy a house, and counteract the effects of redlining and the subprime mortgage crisis as president.”