For a congressman who isn't afraid to start up an investigation, Rep. Darrell Issa (R-CA) sure was cautious when the idea of probing into News Corporation was presented to him.

The House Oversight committee chairman appeared on Fox News Tuesday evening and declined to investigate the Murdoch corporation. News Corp. is facing allegations of whether the company broke the Foreign Corrupt Practices Law and hacked into the phones of 9/11 victims.

Oversight committee ranking member Rep. Elijah Cummings (D-MD) and other members of his panel called on Issa to probe News Corp earlier in the week. But the California Republican seemed disinterested in fulfilling their hopes.

"This is being looked at by the Justice Department," Issa said to anchor Bret Baier, who the congressman praised for asking the question about his employers. "This is being looked at by the Senate, and we’re keeping and eye on it. But at the same time, this is a story about a unit in another country. And we want to make sure we don’t enter the ground that is most inappropriate for us, which is we don’t start picking on media whether they’re the left or the right just because we can."

Issa's decision to "not pick on the media" contrasts with his to demand a retraction from the New York Times reporting on his conflict of interests in late August. And when interviewed last year by Think Progress, Issa stated that he trusts News. Corp because he "personally knows Rupert Murdoch."

WATCH: Video from Fox News, which appeared on September 13, 2011: