Mayor Antonio Villaraigosa -- Radio Silence on SHEEN-GATE [Video]

L.A. Mayor Antonio Villaraigosa might have a future in boxing -- because he bobbed and weaved like a real pro Sunday morning as soon as a photog even mentioned the name Charlie Sheen.

Villaraigosa was in D.C. leaving an interview with "Face the Nation" when he was asked to clarify what really went down in Mexico with the "Anger Management" star.

Villaraigosa's version: He and Charlie met for a quick three-minute chat, snapped a photo together and NOTHING more.

Charlie's version: The mayor's straight-up lying ... the two of them spent hours partying and boozing with hot chicks in his hotel room -- and that's where they snapped the infamous Twitter pic (below).

In the video, Villaraigosa clearly doesn't want to answer the question. But what's interesting is what he doesn't say ... specifically, he NEVER once denies the actor's claims.