Stephen Colbert flat-out called for President Trump's resignation ... the prez admittedly shared classified intel about ISIS with Russian diplomats.

Colbert obliterated Trump during his Monday night monologue after the Washington Post reported the prez had leaked the info. Tuesday morning, Trump tweeted he had "the absolute right" to do so.

The 'Late Show' host disagrees, strongly, but did find a silver lining ... "The good news: Trump found the leaker."

The Trump-Colbert feud -- the gift that keeps on giving.