Though he has received a hero’s welcome from Democrats for his role in the midterms, Mr. Bloomberg is plainly an uncomfortable match for a progressive coalition passionately animated by concern for economic inequality and the civil rights of women and minorities.

In the interview Friday — his first extended comments on his thinking about a 2020 presidential run — Mr. Bloomberg expressed stubbornly contrary views on those fronts. He criticized liberal Democrats’ attitude toward big business, endorsing certain financial regulations but singling out a proposal by Senator Elizabeth Warren of Massachusetts to break up Wall Street banks as wrongheaded. He also defended his mayoral administration’s policy of stopping people on the street to search them for guns, a police tactic that predominantly affected black and Latino men, as a necessary expedient against crime.

And while Mr. Bloomberg expressed concern about allegations of sexual misconduct that have arisen in the last year, he also voiced doubt about some of them and said only a court could determine their veracity. He gave as an example Charlie Rose, the disgraced television anchor who for years broadcast his eponymous talk show from the offices of Mr. Bloomberg’s company.

“The stuff I read about is disgraceful — I don’t know how true all of it is,” Mr. Bloomberg said of the #MeToo movement. Raising Mr. Rose unprompted, he said: “We never had a complaint, whatsoever, and when I read some of the stuff, I was surprised, I will say. But I never saw anything and we have no record, we’ve checked very carefully.”

Mr. Bloomberg said the media industry was guilty of not “standing up” against sexual misconduct sooner, but declined to say whether he believed the allegations against Mr. Rose. “Let the court system decide,” he said, while acknowledging that the claims involving Mr. Rose might never be adjudicated in a legal proceeding.