Nice, France - Princess Charlene of Monaco, who has been receiving specialised care outside the principality, is still some months away from a full recovery, the palace said.
Charlene, the wife of Prince Albert II, is being treated for extreme fatigue away from her family after returning to Monaco in November following months away in South Africa.
Her absence from Monaco's annual national day in November, the biggest annual event in the palace calendar, had fuelled new concern over her health, but also speculation about the state of the couple's marriage.
The princess "is recuperating in a satisfactory and reassuring manner, although it may take a few more months before her health has reached a full recovery", a palace statement said.
Albert and the couple's children had visited the royal during the Christmas holidays, it said, asking for the family's privacy to be respected.
Prince Albert had himself told People magazine in November that Charlene, 43, had needed treatment outside Monaco but did not go into details about the nature of her health problems.
"She was clearly exhausted, physically and emotionally. She was overwhelmed and couldn't face official duties, life in general or even family life," he told the magazine.
The former South African Olympic swimmer married Prince Albert in 2011, after first appearing with him at the 2006 Winter Olympics in Turin.
Initially hailed as a fairytale match for a prince long described as the world's most eligible bachelor, the couple has been dogged by rumours ever since they got married.
There were claims, denied by the royal palace, that Charlene tried to vanish on the eve of the wedding.
Albert is the son of Prince Rainier III and Grace Kelly, an American film star who died in a car accident in 1982.