Mr. Burnett did not respond to a telephone message left at the office of his production company, and a Fox spokesman declined to expand on Mr. Burnett’s comment.

Image The host Kevin Pollak on the set of “Our Little Genius.” Retaped episodes of the game show could eventually be broadcast. Credit... Mathieu Young/Fox

In its own statement, Fox said that it respected Mr. Burnett’s due diligence and his decision to withdraw the episodes. “We agree there can be no question about the integrity of our shows,” the statement said. “While these episodes will not air, the families who participated in the show will receive their winnings, and we are grateful for their participation.”

The sudden withdrawal of the program just days before its debut and the disclosure that “information was relayed to contestants” raises obvious inquiries about whether the contestants were given answers to the quiz questions. “Our Little Genius” has drawn criticism from psychologists and advocates for children who say they think it places unhealthy pressure on the contestants to win a game that offers their family “life-changing money,” according to the Fox promotions.

Two people close to the production  who spoke on the condition of anonymity because they were not authorized by the production company or the network to speak to the news media  said that contestants were not given answers. But contestants could have benefited from other information, like the topics to be covered or the questions that would be asked.

The issue of whether contestants were given answers or were otherwise directed to fake the outcome of a supposedly fair competition was behind the quiz show scandals of the 1950s. Congressional inquiries into the scandals led to a federal law prohibiting the fixing of such shows.