"If evidence comes out through this exhaustive inquiry where you're giving evidence under oath -- if he did breach the ministerial code -- then clearly that's a different issue and I would act," Cameron told The Daily Telegraph.
"As things stand, I don't believe Jeremy Hunt broke the ministerial code."
During the Leveson Inquiry, News Corp. was called on by a House of Commons motion in March 2011 to abandon its bid for BSkyB. NewsCorp. already owned 39.1 percent of the company.
Hunt was accused of having an inappropriate connection with the deal after the Leveson Inquiry released e-mails between Hunt's special adviser, Adam Smith, and News Corp. Public Affairs Director Frederic Michel, which Cameron said indicated Smith had "acted inappropriately." Smith resigned Wednesday.
"I don't think it would be right in every circumstance if a special adviser gets something wrong to automatically sack the minister," Cameron said. "I think he's doing an excellent job on the Olympics and, frankly, I do think people deserve to have these things looked into properly."
The BBC reported Cameron has rejected claims there was a plan to approve the News Corp. bid to acquire BSkyB in exchange for positive press in Murdoch newspapers.
"It would be absolutely wrong for there to be any sort of deal and there wasn't." he said. "There was no grand deal."