Lesley Stahl and two other “60 Minutes” correspondents said on Friday that they would remain in their posts, ending days of speculation about whether a roiling crisis at the CBS News program would leave it entirely deprived of on-air stars.

In a joint email to the show’s staff, Ms. Stahl, Bill Whitaker and Jon Wertheim said they would “stay and fight” in order to “repair and preserve” the reputation of the country’s top-rated news program.

“Here’s why we are staying: We don’t want to see ‘60 Minutes’ die,” they wrote.

But the correspondents also expressed deep frustration with the decision by Bari Weiss, the CBS News editor in chief, to fire Tanya Simon, the show’s executive producer, and several longstanding producers and correspondents, calling those exits “heartbreaking.” And they warned that if the program lost its editorial independence, “we leave.”

Ms. Weiss’s moves — including the appointment of Nick Bilton, a tech journalist and filmmaker with no broadcast news experience, as the program’s new leader — shocked the “60 Minutes” newsroom. In a meeting on Monday, the longtime correspondent Scott Pelley assailed Mr. Bilton and accused Ms. Weiss of “murdering” the show; he was fired the next day.

In the days since, Mr. Bilton scrambled to persuade Ms. Stahl, Mr. Whitaker and Mr. Wertheim to remain. At a dinner with Ms. Stahl, Mr. Bilton offered assurances that he would preserve the show’s journalistic rigor; on Thursday, he emailed the staff promising that “60 Minutes” would stay editorially independent from its parent company, which is controlled by the tech scion David Ellison, who appointed Ms. Weiss.