The cancellation on Mr. Letterman’s show follows by a few weeks the cancellation by Mr. Cosby of a guest appearance on the Queen Latifah daytime talk show. In that case, the show reported that the change was made at Mr. Cosby’s request. Mr. Cosby did appear on Stephen Colbert’s show on Sept. 24 on Comedy Central and with Jimmy Fallon on NBC’s “Tonight” show on Aug. 18.

On Thursday, The Washington Post published a first-person article online by a former actress named Barbara Bowman, who said that Mr. Cosby had drugged and raped her on more than one occasion in the mid-1980s during a period when he was mentoring her as a young actress. That was at the same time he was starring in the biggest hit on television, “The Cosby Show.”

Ms. Bowman’s allegations follow similar charges by other women, one of whom, Andrea Constand, filed a civil suit against Mr. Cosby in 2005, which promised to include testimony from 13 other then-unnamed women. One of those was Ms. Bowman, she said in her article. The suit was settled for an undisclosed amount. Both Mr. Cosby and his lawyers have issued denials of the charges at various points.

This week, an effort to kick up some favorable attention for Mr. Cosby — in the form of a thread on Twitter instigated on behalf of Mr. Cosby — blew up into a chorus of nasty comments accusing him of sexually assaulting women. The stand-up comic Hannibal Buress stirred a new round of attention to the allegations when he assailed Mr. Cosby in a routine on stage in Philadelphia last month.

The fallout may continue for Mr. Cosby. NBC had announced a new project with the comedian in which he would star as the patriarch in a new multigenerational sitcom. That project’s status has not changed officially, but it does not have a script, according to NBC.