Fox, the network that airs the show “Empire,” is standing by Jussie Smollett, one of the drama’s stars, amid a swirl of questions about whether the attack he reported late last month occurred as he said.

“Jussie Smollett continues to be a consummate professional on set and as we have previously stated, he is not being written out of the show,” 20th Century Fox Television and Fox Entertainment said in a joint statement released on Wednesday.

A representative for Mr. Smollett declined to comment.

Multiple outlets had reported that Mr. Smollett was being written out of the show in the aftermath of an announcement by the Chicago police that the trajectory of the investigation had changed.

[Read our timeline about the Jussie Smollett case here.]

The police have said they are now seeking to interview Mr. Smollett again after hearing the accounts of two brothers, initially identified as possible suspects in the attack and who were later released. Multiple media outlets have reported that the brothers told investigators that Mr. Smollett staged the incident — in which they participated — in the pursuit of public attention.