If you want to register your work, you need to declare usage of AI

In the somewhat recent decision of the copyright office in re: Théâtre D’opéra Spatial, an
artist was denied copyright registration for not declaring that he used an AI to generate a part of the image. The board found:

After carefully examining the Work and considering the arguments made in the First and
Second Requests, the Board finds that the Work contains more than a de minimis amount of AI-generated content, which must be disclaimed in an application for registration. Because
Mr. Allen has refused to disclaim the material produced by AI, the Work cannot be registered as
submitted.

Likewise, earlier, the copyright office revoked a registration earlier with in re: Zarya of the Dawn for usage of undeclared AI content, and re-issuing a registration only for the non AI-generated text:

We conclude
that Ms. Kashtanova is the author of the Work’s text as well as the selection, coordination, and
arrangement of the Work’s written and visual elements. That authorship is protected by
copyright. However, as discussed below, the images in the Work that were generated by the
Midjourney technology are not the product of human authorship. Because the current
registration for the Work does not disclaim its Midjourney-generated content, we intend to
cancel the original certificate issued to Ms. Kashtanova and issue a new one covering only the
expressive material that she created.

Declaration of AI-generated content is not to be confused with attribution. It is a declaration that you did not create this aspect and do not claim copyright in that aspect. Attribution is academically telling who made the material you cite.

You can not own copyright in AI-generated content in the first place, but you can have copyright in any other aspects of a work, such as the text in the case of Zarya of the Dawn.