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Mayor Pete Buttigieg had the most interesting convo Wednesday on the streets of New York City -- problem is ... it was all in Maltese!

The presidential candidate ran into a dude who happens to be a president himself -- president of a Maltese club in Astoria, NY.

The South Bend Mayor speaks the official language of Malta, which is not surprising because it's a derivation of English, Italian and French ... languages in which he's fluent.

We have our Malta spies, so we know roughly how the conversation went down. The guy asks Pete if his family is from the island of Gozo. Pete says his fam is from Hamrun, where his grandparents lived a few doors down from Anton Buttigieg -- no relation -- and he became Prez of Malta.

Sounds like Buttigieg is like Smith in Malta.

Anyway ... the guy invites Pete to speak to his org, and sweetened the pot by offering him pastizzi from an Astoria restaurant -- it's a Maltese national snack.

This is only a partial clip of the conversation. You can only handle so much Maltese on TMZ.