Father Giovanni Cavalcoli, a theologian known for his hardline views, made the comments on October 30, the day central Italy was struck by a 6.6-magnitude quake -- the most powerful to hit the country in 36 years --
according to Italian media.
It was the third major quake in the same region in just over two months.
Cavalcoli said on Radio Maria that the seismic shocks were "divine punishment" for "the offence to the family and the dignity of marriage, in particular through civil unions".
The radio station distanced itself from his views and late Friday the Vatican issued a stinging rebuke, saying the idea of a vengeful God was "a pagan vision" dating from "the pre-Christian era".
Archbishop Angelo Becciu, number two in the Vatican's powerful Secretariat of State, said Cavalcoli's comments were "offensive to believers and disgraceful for non-believers", in remarks reported by Italian media.
Becciu asked for forgiveness from quake victims and reminded them they had the "solidarity and support" of Pope Francis.
But Cavalcoli has refused to back down, insisting to another radio station that earthquakes are indeed caused by "the sins of man" and telling the Vatican to "read their catechism".
Legislation allowing gay civil unions in Italy only took effect last month, making it the last country in Western Europe to legally recognise same-sex relationships.