The Pope has telephoned a senior Italian bishop sent a bullet in the post last week to offer his support.
Monsignor Bagnasco is the Vatican's chief spokesman against the law
Archbishop Angelo Bagnasco has come under attack for speaking out against a proposed law giving greater rights to unmarried couples, including gays.
The threats against the archbishop began last month when the doors of his cathedral in Genoa, northern Italy, were daubed with graffiti.
The Vatican opposes a draft bill on civil unions currently in parliament.
Monsignor Bagnasco received an envelope at the end of last week containing the bullet along with a picture stamped with a swastika, media reports say.
Police have now assigned an armed guard to the bishop.
In his phone call, the Pope expressed his solidarity with Monsignor Bagnasco, the Vatican said.
He also urged him to continue his work for those human and religious values without which, he said, it was impossible to build a true, free and stable democracy.
The fact that the Vatican has let it be known that the Pope personally lent his support to the embattled bishop suggests just how seriously the Catholic Church is taking the increasingly vitriolic nature of the attacks on its stance on the proposed law, says the BBC's Mark Duff in Milan.
Italian President Giorgio Napoletano also intervened on Monday, assuring the Vatican that Italy would not leave the bishop to stand alone in the face of "vile threats".
Monsignor Bagnasco recently became president of the Italian bishops' conference - and as such the chief spokesman for the Vatican's vehement opposition to the new law, our correspondent says.
The Catholic Church says the legislation undermines the position of traditional marriage in society.
The first graffiti appeared after the archbishop referred to incest and paedophilia as examples of what can go wrong when the Church's moral certainties are ignored.
Following the comments, Church officials stressed he had not meant to draw any link between the rights of unmarried couples and incest or paedophilia.