Trump Says Obama Gave Out Classified Information About Aliens

President Trump says Barack Obama would be wise to keep his mouth shut about aliens ... 'cause he says Obama gave out top secret information on a podcast where Obama said extraterrestrials were real.

Check out this exchange between Trump and FOX News' Peter Doocy Thursday aboard Air Force One.

Peter asks POTUS if he's "seen any evidence of non-human visitors to Earth" given that Obama recently came out and said aliens were real.

Trump shoots back ... "Well, he gave classified information, he's not supposed to be doing that."

Peter asks if Trump is saying aliens are in fact real -- even though Obama later walked back his comments -- and Trump says he doesn't know if aliens are real or not and only knows that Obama "took it out of classified information" and "made a big mistake."

The Prez says he doesn't have an opinion on the existence of extraterrestrial life -- Obama says the size of the universe makes the chances pretty good -- but admits lots of folks believe in aliens.

Trump also hinted at disclosure ... saying he may get Obama "out of trouble by declassifying."