Some scientists have suggested that the breakthrough could be used to help older women conceive, or reverse the symptoms of the menopause.

The BBC's Niall Dickson: "For many women this technique offers hope"

But Professor Roger Gosden, of Leeds University says the technique should only be considered as an emergency measure for children and younger women who are about to lose their future fertility.

He said: "There is much speculation about about how this technique can be used in other ways - and maybe one day it will be.

"But we wouldn't want to put a perfectly healthy woman through a procedure which was still experimental.

"We certainly haven't aimed to reverse the menopause because we feel that the priority is to help women conceive using their own eggs."

A segment of ovary from a 30-year-old American woman, Margaret Lloyd-Hart, which had been removed and frozen several years ago, was grafted back inside her in February by Dr Kutluk Oktay at New York Methodist Hospital.

Margaret Lloyd-Hart following her operation

Dr Oktay is a former research fellow of Professor Gosden, who pioneered the technique

Doctors now report that it has taken successfully and Ms Lloyd-Hart has started ovulating, although she does not yet have a full menstrual cycle.

Experts at Leeds and elsewhere were keen to stress that the release of an egg did not mean that Ms Lloyd-Hart could have a successful pregnancy.

The 30-year-old who lives in Arizona, had an ovary removed last year to treat a benign medical condition. Her other ovary had been taken out when she was 17 because of a cyst.

Experts say the new technique could have a greater effect on human fertility than the advent of in vitro fertilisation (IVF) 20 years ago.

The grafts could be used to treat sterility caused by the onset of premature menopause and protect fertility in patients undergoing cancer treatment.

Dr Kutluk Oktay: Ground-breaking

Dr Oktay said: "Children as young as four years old are having their ovaries frozen so that, in the future, they can have the tissue returned to their bodies."

The grafts could also delay the menopause so that even elderly women could conceive.

And they may eventually prove a safer substitute for the widely-used hormone replacement therapy (HRT).

But Professor James Drife, president of the Royal College of Obstetricians and Gynaecologists, said that the production of an egg did not automatically mean a pregnancy was possible.

He told the BBC: "There are many steps between successful hormonal production and the release of the egg and the fertilisation of the egg. The state of the egg is absolutely critical."

He added that it was unsure whether it would ever prove more effective than currently-available HRT.

Prof Gosden will report on the successful operation at the annual meeting of the American Society for Reproductive Medicine in Toronto, Canada.

Tony Rutherford:"Patient selection is very important"

The society's president Larry Lipshultz said: "This should give great hope to women suffering from ovarian and other cancers, and may lead to successful treatment for other causes of infertility."

The new procedure also opens up the possibility of donor ovaries being transplanted into infertile women.

The long-term applications of the technique are likely to reopen an ethical debate similar to that which greeted the news last year that a 60-year-old woman had become pregnant after egg donation.

Ovary grafts fall outside the control of the Human Fertilisation and Embryology Authority, which is concerned only with mature eggs and sperm, while ovaries contain immature eggs.