Washington — The N.B.A. has long tried to portray itself as the most progressive sports league in the United States. Adam Silver, the league’s commissioner, took another step in trying to reinforce this image on Thursday, saying that the N.B.A. had set a goal: at least half of its new referees should be women.

“I’m not sure how it was that it remained so male-dominated for so long because it’s an area of the game where physically, certainly, there’s no benefit of being a man, as opposed to a woman when it comes to refereeing,” Silver said to a gathering of The Economic Club of Washington, D.C.

He added that he wanted the same for coaches: “There’s no reason why women shouldn’t be coaching men’s basketball.”

Silver took part in a moderated discussion with David M. Rubenstein, the president of The Economic Club, at the Capital Hilton in front of an audience of about 500, mostly business executives. The appearance comes at a sensitive time for the N.B.A. The league has seen a boom in recent years, buoyed by an offensive explosion as well as the emergence of several marketable stars.

But now the league has hit some speed bumps. Television ratings are down about 9 percent for this year’s playoffs, according to Nielsen, although this does not include viewers on smartphones and other such devices. For the first time since 2005, the N.B.A.’s biggest star, LeBron James, will not be on its biggest stage, after the Los Angeles Lakers didn’t make the playoffs.

And there has been grumbling about the lack of parity in the league, after the Golden State Warriors signed Kevin Durant in 2016, just after the team had won a record 73 games in the regular season and a championship the year before that.

But much of the recent complaints about the league have had to do with officiating, particularly in the Western Conference Semifinal series between the Warriors and the Houston Rockets. The relationship between players and referees has been unusually tense this season, inflamed by the ability of modern technology to catch mistakes in high-definition replays and then for them to play in an endless loop on social media. According to an ESPN report last month, the Rockets believe officials robbed them in Game 7 of last year’s Western Conference Finals against the Warriors, even going so far as to draft a memo sent to the league detailing why.

But Silver didn’t address those criticisms; only the effort to make the officiating ranks more gender inclusive.

There is still a long way to go before the gender makeup of basketball officials at the highest level changes in a meaningful way. Currently, according to Silver, there are three female officials working N.B.A. games. Two of them comprise the last five referee hires from the G-league, the N.B.A.’s developmental system. There has been at least one instance of a star player not taking kindly to a female referee: In 2015, Chris Paul, then playing for the Los Angeles Clippers, was upset by a technical foul called by Lauren Holtkamp. After the game, Paul said to reporters, “This might not be for her.” He was fined $25,000 for the comment.