Trustworthiness "became a big problem" for Michael Flynn and led to his resignation as national security advisor, Senate Foreign Relations Committee Chairman Bob Corker told CNBC on Tuesday.

"On one hand [he] was setting up a national security council in a true interagency way which hasn't been done in a long, long time. So I applaud his efforts in that regard," Corker said on "Squawk Box."

But on the other hand, the Tennessee Republican said, "the credibility issue became a big problem [for Flynn] when it was revealed what conversations were with the Russian ambassador. And he stepped away."

Less than a month on the job, Flynn abruptly quit as President Donald Trump's national security advisor Monday night after disclosures that he misled Vice President Mike Pence and other senior officials about his communications about sanctions with Russia's ambassador to the United States.

Keith Kellogg, a retired lieutenant general and a top policy advisor to Trump during the campaign, was appointed as acting national security advisor.

Two other candidates being considered on a permanent basis are retired Navy Vice Adm. Robert Harward and David Petraeus, a retired general and former director of Central Intelligence.

Corker told CNBC he does not have a favorite.

"I don't know the other two individuals as well as I know David [Petraeus]. He's from my standpoint, an American hero. Somebody I respect greatly. No one is more knowledgeable regarding issues around the world," the senator said.



Petraeus resigned as CIA chief in 2012, under fire for sharing classified information with his biographer, with whom he was having an extramarital affair. He later pleaded guilty to mishandling classified information, and was fined and put on probation.