Agree with Cassa'. Columbo shows a certain insolence (excellent acting here) when he tells Steiger that he doesn't speak Italian.

As I see it, Steiger's character is attempting to draw Columbo into a little web of solidarity, by invoking their common language. And when Columbo responds by pretending that he does not speak Italian, he is intentionally lying to the mafioso's face -- note how Columbo glares at him -- as a way of telling him, "You are a criminal and I am a policeman -- so, I do NOT consider you my paisan!"

Steiger probably knows perfectly well that Columbo speaks Italian, which is why the insult stings.