Authorities in Turin, northern Italy, have refused to register the baby of a lesbian couple.
Chiara Foglietta, a Turin councillor, underwent artificial insemination in Denmark and gave birth last Friday to baby boy Niccolo Pietro.
Italian law sets strict rules for fertility treatment, making it available only to stable heterosexual couples.
But Ms Foglietta has refused to pretend sex with a man led to Niccolo's birth.
In a Facebook post, the centre-left councillor said "the staff [at the public records office] tell me 'you should declare that you had union (sexual intercourse) with a man, to get your boy registered. There is no formula allowing you to say that you had artificial insemination'."
She said Niccolo was born because she and her partner Micaela Ghisleni wanted a baby, and "he is our son".
"But to get him registered at the public records office I have to tell a lie," she said, adding that "every child has the right to know his or her own story, the combination of events that created him or her".
Ms Foglietta received sperm from an anonymous donor at the clinic.
But many fertility procedures allowed in other EU countries are banned in Italy, under a 2004 law. There can be no screening or freezing of embryos; no sperm or egg donation; nor surrogacy or embryo research. The treatment is only provided for "stable heterosexual couples" shown to be clinically infertile.
Commenting on the case of Niccolo, Turin mayor Chiara Appendino said "the law currently does not provide for recognition of the sons and daughters of homosexual couples born in Italy".
Quoted by the Italian daily Corriere della Sera, she said, "Personally I am in favour and willing to proceed with registration, but with this current legal vacuum the rights of the parents and children cannot be guaranteed".
Italy's fertility rate is among the lowest in the EU.
In 2017 the average number of children per woman in Italy stood at 1.34, compared with 1.46 in 2010, the national statistics agency Istat reported. In 2017 there were 183,000 more deaths than births in Italy.
France has legalised gay marriage and gay adoption, going further than the LGBT rights in Italy. But France, like Italy, does not recognise children born to lesbian couples through artificial insemination.