Washington (CNN) – Will an apology be enough to soothe the strained relations between the CIA and members of the Senate Intelligence Committee? It’s a critical lingering question in the rare public spat between the intelligence agency and the lawmakers charged with the agency’s oversight.

Tempers on the committee flared in recent months over reports that the CIA spied on computers used by intelligence committee staffers. A CIA inspector general’s report confirmed these reports this past week, prompting CIA Director John Brennan to apologize to committee members Thursday. However, some members aren’t satisfied, citing Brennan’s previous remarks that batted down the spying accusations

“I don't think an apology is enough,” Independent Sen. Angus King of Maine told CNN’s Candy Crowley on “State of the Union.” “I think we've really got to have some serious discussions about John Brennan, find out what he knew about this when he was making those statements, what he knew about it at the time. I'm not calling for his resignation, but I'm pretty skeptical right now.”

In contrast, the White House reconfirmed support of Brennan.

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