Monti told Sky TG24 TV on Sunday that issues involving personal dignity are more important that economic reforms.
But he stressed that his coalition forces, which include pro-Vatican centrists, came together to work on the more "urgent" task of achieving economic growth in recession-mired Italy.
He says the new Parliament will have a greater role than the government in dealing with gay rights. Monti didn't express his personal opinion on gay marriage.
Same-sex marriage isn't permitted in Italy. The Vatican, which carries significant influence in Italian politics, opposes same-sex marriage.