Mr Rees-Jones, a bodyguard employed by the Fayed family, suffered severe facial and head injuries, but these were not as serious as early reports suggested. In particular, officials have denied a leak from the Pitie Salpetriere hospital last week which suggested that his tongue was severed and he may never talk again.
The former paratrooper's mother and father, Jill and Ernie Rees-Jones, issued a statement in Paris yesterday in which they revealed that their son had a 10-hour operation last Thursday "for facial reconstruction".
"The operation was a success and he has started on a long road to what we expect will be a full recovery," they said. "It will be some time before he will be able to speak to investigators."
The couple thanked the medical team at the hospital and the Fayed family, which has been paying the bills for their stay in Paris.
A street or square in Paris - possibly close to the site of the crash last Sunday week - is likely to be named after the princess.
A small square, beside the exit from the underpass in which the princess's car crashed, was due to be renamed after the opera singer Maria Callas this week, but this was delayed yesterday by Jean Tiberi, the Mayor of Paris. The town hall said he intended to consult with the families of the crash victims before proposing a site to the city council.
Officials added that the square near the underpass could now be reserved for the princess but that this would depend on the views of her family. Parisians have already turned the larger square above the tunnel itself - the Place de L'Alma - into an impromptu shrine to the princess and many have called for it officially to be given her name.
Police and investigators yesterday refused to say when they would release the results of the third blood-alcohol test conducted on Henri Paul, the driver of the crashed car. Earlier tests, which were made public within one day, suggested that he was driving with more than three times the permitted level of alcohol in his blood.
His family asked for a further test last week and a British expert retained by the Fayed family said the earlier findings were "unreliable". A third test was conducted last Friday.
Investigations into the mobile phone records of the photographers have determined that none of them called the emergency services after the crash.Reuse content