The executive added that the company would release people from existing nondisclosure agreements related to those matters on a case-by-case basis.

The use of nondisclosure agreements for workers who make complaints of sexual harassment or discrimination has become a point of contention in the wake of the #MeToo movement, and The New Yorker has been at the forefront of the discussion. The magazine won a Pulitzer Prize in 2018 for Ronan Farrow’s investigation into allegations of sexual misconduct by the film producer Harvey Weinstein, which involved the use of nondisclosure agreements to silence his accusers. (The Times reporters Jodi Kantor and Megan Twohey were also awarded the Pulitzer that year for their investigation into Mr. Weinstein.)

Mr. Weinstein is currently on trial, accused of rape, in Manhattan.

During the Democratic presidential primary debate in Las Vegas on Wednesday, Senator Elizabeth Warren criticized Michael R. Bloomberg for the use of nondisclosure agreements at his company, Bloomberg L.P. He had refused to release some female former employees from agreements they signed after accusing him of harassment and discrimination. (Mr. Bloomberg announced on Friday that he would release three women from nondisclosure agreements if they contacted the company.)

Condé Nast’s decision to limit the use of nondisclosure agreements was reported earlier by The Daily Beast.

The union that represents employees at The New Yorker and the Condé Nast publications Pitchfork and Ars Technica had proposed that the company drop nondisclosure agreements at the bargaining table for The New Yorker in November, said Susan DeCarava, the president of the union, the NewsGuild of New York.