Democratic presidential candidate John Edwards dropped out of an August debate planned by the Nevada Democratic Party, in part because it was being hosted by Fox News channel.
Ailes used a speech during a Radio & Television News Directors Association Foundation event in Washington to deliver a caution to the candidates, TV Week said.
"The public knows if a journalist's question is unfair. They also know if a candidate is impeding freedom of speech and free press," Ailes said. "If you are afraid of journalists, how will you face the real dangers in the world?"
A candidate -- he never mentioned Edwards by name -- that boycotts a debate because of its media sponsorship, Ailes said, "is making a terrible mistake about journalism" and also runs the risk of alienating voters.