A set of newborn triplets in California is now at the centre of a court battle over the issue of parental rights between a surrogate mother and a man who paid her $33,000 to have a baby via IVF using his sperm and the eggs of a 20-year-old donor.

Surrogate mother Melissa Cook, 47, delivered the premature babies on Monday after she refused to abort one of the embryos as demanded by the father, a 50-year-old man who works as a postal worker from Georgia who is identified in court papers only as "C.M."

Cook, a pro-life advocate, refused to have an abortion and has sued to seek parental rights and keep the third baby.

"I'm healthy, I'm 28 weeks pregnant, the babies are doing great, the three little boys I have inside me," Cook told Fox News before she gave birth.

Under California laws, a gestational surrogate, who carries a donor's eggs, has no parental rights and Cook is challenging the law in court.

"It's an attempt to reduce women to an object, or a breeding animal," said her lawyer, Harold Cassidy, a pro-life and anti-surrogacy lawyer. "You can doctor this up, you can play word games with it, but this is simply and purely the sale of a child."

The contract between Cook and the father stipulated that he would pay her $33,000 and another $6,000 for each additional child.

After Cook gave birth, the babies were immediately taken away from her as a judge awarded parental rights to the father.

"The hospital personnel refused to let Melissa see the children, allow her to know what their condition is, refused to tell her their exact weights, and she is not being permitted to see the children at all," Cassidy said. "We have a mother who loves them, who fought for them, who defended their life, who stands ready to take care of them. You can't tell a mother who gives birth to children that what happens to the children is none of her business."

Court documents showed that last September, the father told his attorney that Cook's visits to a fertility clinic were "draining my finances."

"I do not want to abort twin babies, but I felt that is such possible (sic) to seek aborting all three babies," the father wrote. "I do not want to affect Melissa's health. I do not have any more money in the bank, and my job does not pay great bi-weekly."

According to Cook's lawsuit, "C.M. depleted his life savings paying for the infertility doctors, paying the surrogacy broker, paying the anonymous ova donor, paying the lawyers and putting money into trust for the surrogate," resulting to "his demand that Melissa have an abortion because he could not financially afford the children and was otherwise incapable of raising the children."

Surrogacy contracts allow "selective reduction" or abortion due to medical reasons.

C.M. wrote last November: "My decision made is, requires a selection reduction (sic). I am so sorry."

Cook said she was threatened with legal and financial damages if she did not undergo abortion.

C.M. has refused to discuss the issue outside the courtroom.

"My interest is in protecting my three children. I continue to have concern for the health and welfare of the surrogate and wish to avoid her having unnecessary stress through a public presentation. I have no interest in sensationalising the situation," he said in a statement.

Cassidy is challenging surrogacy and abortion in the U.S., saying surrogacy has been outlawed in most of Europe and Canada.

"Some man who donates sperm on the other side of the country is a stranger to that child, so much so that it is nothing for him to demand that the mother who loves the children he's carrying has to kill one of them," he said.