In recent weeks authorities made it harder for same-sex couples to be legal parents and lawmakers proposed an anti-surrogacy law widely seen as targeting gay couples.
In January, the government issued orders that municipalities stop the registration of most children with same-sex parents, complicating access to schooling and medical services.
Rainbow Families, a group representing same-sex parents in Italy, says its members are parents to around 1,500 children, but that this underestimates the national total.
In some places, already-registered children of same-sex families are now being erased from the records, upon the initiative of prosecutors.
In similar cases previously, judges have routinely ruled against same-sex parents.