* Ban on sperm or egg donation ruled unconstitutional
* Couples brought series of challenges to restrictive law
* Catholic Church opposes non-traditional conception
* Singles, same-sex couples still banned from treatments
By Naomi O'Leary
ROME, April 9 (Reuters) - Italy's constitutional court overturned a ban on using donor sperm and eggs in fertility treatments on Wednesday, knocking down part of a divisive set of restrictions on assisted reproduction.
The court said in a statement the ban breached the constitution, without going into further detail, and lawyers in the case said the ruling was effective immediately.
But Health Minister Beatrice Lorenzin, from the socially conservative New Centre Right party, said parliament would have to debate how the court order could be applied.
Couples in predominantly Catholic Italy have launched a string of legal challenges to restrictions included in "Law 40", passed by the then centre-right government of Silvio Berlusconi in 2004.
Treatments such as artificial insemination and in vitro fertilization (IVF) have become increasingly popular across the Western world.
But in Italy, they have been opposed by a conservative establishment influenced by the Catholic Church, which rejects non-traditional conception and opposes the discarding of embryos with defects, believing an embryo should be treated as a person from the moment of conception.
Initially the law forbade the fertilisation of more than three eggs during treatment, and stipulated that all three had to be implanted simultaneously and could not be screened for genetic disorders.
Those provisions were overturned after legal challenges in 2008 and 2009.
The most disputed aspect of the law, a ban on allowing carriers of genetic disorders to use IVF to screen embryos before implantation, remains in place pending a Constitutional Court decision that is expected after June 18.
The European Court of Human Rights (ECHR) ruled in 2012 that the ban on screening breached the right to respect for family and private life under the European Convention of Human Rights.
The EHCR ordered Rome to pay compensation to a couple who, after the death of their first child from cystic fibrosis, wanted to use the techniques to have a second child free from the disease.
Critics say the restriction throws up an anomaly - because couples are legally allowed to abort a foetus if it is found to have an genetic disorder, but cannot step in at an earlier stage to reject an embryo with defects.
Health Minister Beatrice Lorenzin said parliament would have to debate on how to implement the latest constitutional court ruling, saying there were still questions about respecting donors' rights to anonymity and children's rights to know the identity of their genetic parents.
Supporters of the Italian restrictions often argue that selection of embryos opens the door to eugenics, the practice of engineering the genetics of the population, much discredited due to its association with Nazi Germany.
Under the current law, single people and same-sex couples are banned from using fertility treatments.
The law also outlaws the use of embryos in scientific research, though the Constitutional Court will discuss this on June 18. (Reporting by Naomi O'Leary. Editing by Alessandra Galloni)