Argentina's new president is a handful, but not nearly as much as his hot girlfriend -- who he was feeling up and locking lips with onstage in front of everyone ... and it's all on video.

Javier Milei touched down Friday in the city of Mar de Plata to catch his actress GF Fátima Flórez's live play -- which is apparently named after her, "Fatima 100%." Anyway, afterward ... the prez hopped onstage while people were applauding, and congratulated her himself.

After launching into a speech about the hard times Argentina is about to enter as he kicks off his presidency -- which just started late this year -- he smooched Fátima ... passionately.

They started with just a peck ... but quickly launched into full-blown tongue wars, showing off a ton of PDA to the crowd as they cheered and whistled. Once they were done, Fátima said a few words of her own, thanking her BF and then leaving with him shortly afterward.

This ain't the first time the couple has shown affection in public like this -- they actually tend to do it all the time ... which jibes with Javier's personality in general, AKA a lil' wild.

His presidential victory was seen as game-changing -- but mostly because he's a bit like Donald Trump, in that he's aiming to deregulate much of Argentina's government and ring in a new economic philosophy. Basically, he wants to make Argentina self-sufficient and lean.

He thinks he's already on course to do just that ... a few weeks ago, he devalued Argentina's currency by a whopping 50% -- which Javier says is going to help stabilize their economy.

It's been a bit of a whirlwind term thus far ... and he's just getting started. Buckle up!