“If any of them want to be released from their NDA so that they can talk about those allegations, they should contact the company and they’ll be given a release,” Mr. Bloomberg said in the statement. “I’ve done a lot of reflecting on this issue over the past few days and I’ve decided that for as long as I’m running the company, we won’t offer confidentiality agreements to resolve claims of sexual harassment or misconduct going forward.”

The statement by Mr. Bloomberg did not appear to release all former employees of his media and technology company from such agreements. For instance, it did not say he would allow people to speak out if they had signed nondisclosure agreements after complaining of harassment from any person other than Mr. Bloomberg.

The shift on the nondisclosure agreements came as Mr. Bloomberg’s Democratic rivals campaigned in Nevada on the final day before the state’s caucuses on Saturday. Former Mayor Pete Buttigieg of South Bend, Ind., knocked on doors in the Las Vegas area seeking votes, and former Vice President Joseph R. Biden Jr. joined a cookout and precinct captain training with supportive union members in Las Vegas, where he emphasized his longstanding support for labor.

Senator Bernie Sanders campaigned in California amid the disclosure that he had recently been briefed by intelligence officials on Russian efforts to aid him in the Democratic primary race.

Mr. Bloomberg, who is skipping the first four nominating states and will join the race on Super Tuesday on March 3, faced scathing criticism from his rivals at the debate on Wednesday about his refusal to release women from nondisclosure agreements. Ms. Warren, in particular, confronted him on the issue, asking him: “So, Mr. Mayor, are you willing to release all of those women from those nondisclosure agreements so we can hear their side of the story?” Mr. Bloomberg said he was not.