Mr. Whitaker also wrote an opinion article that same day for CNN’s website with the headline “Mueller’s Investigation of Trump Is Going Too Far.” He said the investigation needed to be limited. Mr. Whitaker, a former college football player, joined the Justice Department in October 2017 after Mr. Trump watched him as a CNN analyst and approved of his television appearances.

World Patent Marketing was founded in 2014 and had the hallmarks of a legitimate business. It used a splashy website and other marketing materials to “create the impression that they have successfully helped other inventors,” the trade commission said in its complaint.

In reality, the commission said, the Miami Beach company failed to make good on almost every promise it made to consumers, and strung them along for months or years after taking their money.

When prospective customers left their contact information on the company website, an employee would call them back and follow a script: The company was an “invention powerhouse” with an “incredible advisory board,” including Mr. Whitaker, a “former United States attorney who was appointed by President George Bush.” Mr. Whitaker had served as the top prosecutor for the Southern District of Iowa, a position he held until 2009.

In joining the board, Mr. Whitaker was quoted in a news release issued by the company as saying that he was honored to be a part of World Patent Marketing because it was a “trusted partner to many inventors.”

In another news release, Mr. Whitaker was quoted as saying that “as a former U.S. attorney, I would only align myself with a first-class organization.”

“World Patent Marketing,” the release continued, “goes beyond making statements about doing business ‘ethically’ and translates those words into action.”