Gov. Kay Ivey of Alabama raised questions on Sunday about a federal plan to transport American passengers of the Diamond Princess cruise ship who tested positive for the coronavirus to a federal center in the state.

Governor Ivey said that the Department of Health and Human Services last week had “inadvertently” publicized the proposal to transport an unspecified number of American passengers to the Federal Emergency Management Agency facility in Anniston, Ala., as early as Wednesday. She said the Anniston center is actually being considered as a back up.

“There were some grave concerns about why the site in Anniston was chosen and how, logistically, this would play out in the event this backup site were to be eventually activated,” Governor Ivey said. “While locating these folks in Alabama is currently a backup plan, this is a serious issue and we need to be fully aware of the facts regarding the potential of housing them in Anniston.”

Senator Richard C. Shelby of Alabama said in a tweet on Sunday that President Trump had told him that “his administration will not be sending any victims of the Coronavirus from the Diamond Princess cruise ship to Anniston, Alabama.”

The exchange came as officials scrambled to monitor thousands of people returning from China. It underscored the apprehension among some about where Americans who have tested positive for the coronavirus would be taken. The city of Costa Mesa, Calif., has gone to court to block state and federal officials, at least temporarily, from placing dozens of people evacuated from Asia in a state-owned residential facility in their community. Mr. Trump was upset that passengers with coronavirus were brought back to the United States, according to administration officials.

Reporting was contributed by Choe Sang-Hun, Elisabetta Povoledo, Austin Ramzy, Motoko Rich, Makiko Inoue, Salman Masood, Mujib Mashal, Isabel Kershner, Tiffany May, Derrick Bryson Taylor, Tess Felder, Amy Harmon, Farah Stockman, Edward Wong, Vivian Wang, Mihir Zaveri, Katrin Bennhold and Constant Méheut.