CANBERRA, Sept 20 (Reuters) - A lesbian couple in Australia are suing their doctor after they had twin girls from an in vitro fertilisation (IVF) procedure when they only wanted one child.

The two women are seeking more than A$400,000 ($340,000) in damages to help pay for the cost of raising the second child, including private school fees, saying they made it clear to their doctor that they only wanted one baby.

The twins are now three years old and the civil case, the first of its kind in Australia, has prompted debate about the value of children and role of parents.

"The litigation involving twins already three years old undermines the importance of parenthood," conservative government Senator Guy Barnett said on Thursday.

"We seem more intent on preserving and pandering to the wishes of adults, than we are in protecting the rights of children," he said.

Barnett called for banning same-sex couples and unmarried women from access to publicly-funded IVF services, sparking a new moral debate ahead of national elections, due at any time.

The case is being heard in Canberra, where letters published in the local Canberra Times newspaper overwhelmingly criticised the legal action after the birth of two healthy children.

"The child's identity is subsumed to the whim of the mother who has bought the sperm and paid the IVF clinic," columnist Angela Shanahan wrote in The Australian newspaper.

"Ultimately the result is the child as product, robbed of its unique identity."

The court has ordered a gag on the identity of the women, who used donor sperm from a Danish doctor for the IVF treatment in 2003 which resulted in the birth of twin girls.

The court has heard that they signed a consent form to allow two embryos to be implanted, but specifically told their specialist they only wanted one embryo implanted.

The court was told the birth of the twins had created considerable stress within the couples' relationship, but lawyers for the doctor said that almost every couple who had a child went through similar strain. ($1=A$1.17) ((Reporting by James Grubel, editing by Miral Fahmy, james.grubel@reuters.com; Reuters Messaging: james.grubel.reuters.com@reuters.net, +612 6273 2730))

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