A Swedish woman has become the world's first to give birth after having a womb transplant, opening up the possibility for thousands of infertile women to have babies, the doctor in charge of the research project said on Saturday.

The unnamed Swede in her mid-30s delivered a healthy baby boy by caesarean section in early September, around two years after receiving a uterus donated by an unrelated, 61-year-old.

She was one of seven women who successfully underwent a womb transplant from a live donor – in most cases the recipient’s mother - and subsequently had in vitro fertilization (IVF) treatment.

"There are some more pregnant," Mats Brannstrom, Professor of Obstetrics and Gynaecology at University of Gothenburg told Reuters. "They are more than 28 weeks pregnant."

Brannstrom said other hospitals around Europe, the United States,  and  had been waiting for results of the Swedish research before beginning their own programs.

"When we have the results of other studies, we will know how effective the procedure is and what the risks are," he added.

Medical advances in treating infertility and helping women to get pregnant have sparked widespread ethical debate, with some critics saying scientists shouldn't "play God". 

Others question the morality of spending huge sums to enable women to get pregnant when they have the option to adopt.

Brannstrom said the treatment, the first available for women who were born without a viable womb or who have had their uterus removed because of cancer, was "a matter of justice".

"If we decide as a society that infertility is a type of disease - which we have - we should try to treat it," he said.

Around 200,000 women in Europe suffer from uterine infertility. Brannstrom said a transplant was "the only solution to the problem" although it was too early to say whether the procedure, which costs around 100,000 euros ($125,000), would become common.

The University of Gothenburg has permission to do 10 womb transplants with up to two full-term pregnancies for each woman.

The university has already treated nine women, two of whom had to have their transplanted wombs removed. All the women treated will have their uteruses removed again after their pregnancies.

"This is the first type of transplant that is temporary," Brannstrom said.

The program's first pregnancy was confirmed in the spring and the baby weighed around 1,775 grams when delivered by caesarean section after the mother developed preeclampsia in the 32nd week of pregnancy.

"The baby screamed right away and has not required any other care than normal clinical observation at the neonatal unit," Brannstrom said in a statement.

"The mother and child are both doing well and have returned home. The new parents are of course very happy and thankful."