ROME — Italy’s ban on screening embryos for diseases before they are implanted in a womb violates the rights of a couple whose first child was born with cystic fibrosis, the European Court of Human Rights ruled Tuesday.

The court’s finding in favor of the Italian couple triggered fresh calls among Italian politicians for a less restrictive law regulating artificial procreation.

Following fierce lobbying by pro-Vatican centrist parties, Italy’s Parliament passed a law in 2004 that allows couples to use in vitro fertilization for infertility but bans pre-implantation diagnosis of embryos. Vatican teaching forbids artificial procreation methods.

The court concluded it was ‘‘inconsistent’’ that Italians could abort a fetus with defects but not test an embryo before implantation, as the couple had wanted to do. The couple who challenged the law before the Strasbourg court had discovered they are healthy carriers of cystic fibrosis when their daughter was born in 2006 with the inherited disorder.

When the mother became pregnant again in 2010, she had the fetus aborted when it was found to have cystic fibrosis. The couple then hoped to use medically assisted procreation with genetic screening to avoid transmitting the disease to their children. But Italy’s law forbids that, so they took their quest to the court.

The court noted that the Italian government was trying to ‘‘avoid the risk of eugenic abuses’’ with the law but said it interfered with the couple’s ‘‘right to respect for their private and family life.’’

Italy has one of Europe’s strictest rules for artificial procreation.