The Army is not investigating Lt. Col. Alexander Vindman, a key national security official who was fired and escorted from the White House last week, Army Secretary Ryan McCarthy said at the National Press Club on Friday.

Why it matters: Firing Vindman was one of Trump's first acts of retribution against officials who testified at his House impeachment hearings. After Vindman's ouster, Trump made it clear that what happens next in Vindman’s career is "up to the military."

EU Ambassador Gordon Sondland , a standout witness in Trump's impeachment inquiry, was also fired last Friday.

, a standout witness in Trump's impeachment inquiry, was also fired last Friday. Vindman testified that Trump's July 25 call with Ukrainian President Volodymyr Zelensky was "improper," and Sondland testified during the House impeachment trial that he had worked with Rudy Giuliani "at the express direction" of Trump on matters involving Ukraine.

What he's saying: McCarthy said that Vindman is on "a bridging assignment for a couple months" within the U.S. Army's department headquarters, after which he will head to "a senior service college" this summer. "And there's no investigations there," McCarthy added.

Flashback: Speaking to a group of reporters in the White House on Tuesday, Trump said of Vindman: "We sent him on his way to a much different location. And the military can handle him any way they want."

The president added that chairman of the Joint Chiefs of Staff Gen. Mark Milley "can have him and his brother also."

When pressed on how the military would handle Vindman's reassignment, Trump said, "That's going to be up to the military, we'll have to see. But if you look at what happened, they're going to certainly, I imagine, take a look at that."

Go deeper: Trump justifies firing Vindman for being "insubordinate"