The NSA is not looking through former President Jimmy CarterJimmy CarterWas US-China engagement premised on Chinese political liberalization? Pat Robertson steps down as '700 Club' host after 60 years Carter, the longest living former president, celebrates 97th birthday MORE’s emails, its director Gen. Keith Alexander said Tuesday night.

Asked about Carter's claims of NSA spying Tuesday night on Fox News’ “Special Report with Bret Baier,” Alexander said: “Well, we're not.

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“So he can now go back to writing emails.”

If Carter’s claim were true, Alexander said it would be “illegal.” 

“I mean, reality is we don't do that. And if we did, it would be illegal and we would be found, I think, held accountable and responsible.”

Carter claimed on NBC’s “Meet the Press” Sunday that he suspects the NSA might spy on his emails. Because of his fears, he said he sends messages to foreign leaders through the regular postal service instead.

“I have felt that my own communications were probably monitored. And when I want to communicate with a foreign leader privately, I type or write the letter myself, put it in the post office and mail it,” Carter said, “because I believe if I sent an email, it will be monitored.”