Facebook businessmen Patrick J. Duffy and Jimmy Mutakula have requested an investigation of Bill O'Reilly's May 21 broadcast.
Under federal rules, broadcast personnel are required to avoid sensitive information or material during news broadcasts in the space of 15 seconds.
The reasons under which both men were asked to leave the program are unclear. The network they were asked at that point is not known. The pair is also seeking an investigation into breaches of their employment contracts.
Those allegations are likely to attract a grand jury investigation into potential abuse of power.
Fox News has been embroiled in controversy since the original story about Tapper's invitation to O'Donnell and former President George W. Bush was published in 2007.
On Sunday's show, Tappers said that O'Doherty should have been removed from his job, and they admitted their mistake.
“Unfortunately, we made the mistake, and we are taking it very seriously,” Tapperton said.
In an interview, Tipper Gore, Gore's employer, said:
"We are very angry at the source of this report and are sincerely apologizing for the mistakes our company made.".