France's first lady is making progress in a hospital where she is receiving care following a gossip magazine's report that President Francois Hollande was having a secret affair with an actress, according to a spokesman.

Valerie Trierweiler was admitted to hospital on January 9 for rest after the weekly Closer's report about Hollande and Julie Gayet, an actress.

"I can tell you Madame Trierweiler is still in the hospital, and her doctors will determine when she can leave," Patrice Biancone, her spokesman, said in a phone interview with the Associated Press news agency.

Trierweiler's condition is progressing: "She has six days of rest behind her - that counts, after all," he said, without elaborating.

It alleged that Hollande, wearing a helmet with darkened visor, was sneaking into an apartment near the presidential palace by motorcycle to meet Gayet.

The allegation has dented a tradition among French media of ignoring the private lives of public figures.

Hollande has acknowledged "painful moments" in his relationship with Trierweiler, and said the question of who the first lady is would be clarified before his trip on February 11 to the US for a state visit that she had been expected to attend.

Visits 'forbidden'

Biancone appeared to suggest that Hollande had not visited Trierweiler.

"All visits have been forbidden ... except for the family - and even then, just her son," Biancone said, declining to specify which one of Trierweiler's three sons from her previous marriage had.

He did not identify the hospital, or indicate whether the president had been in direct communication with her, saying that was a private matter.

Asked about the matter at a news conference on Tuesday, Hollande said his "indignation is total" about the report, but stopped short of denying the allegations or saying whether he would sue Closer.

Hollande, 59, is a life-long bachelor, but has four children with former presidential candidate Segolene Royal - a fellow Socialist.

He and Trierweiler, a 48-year-old journalist, have lived together since 2007.

While they are not married, she occupies the so-called madame wing of the presidential palace, travels abroad with Hollande, and functions as the first lady.

An official in Hollande's office said Trierweiler had been hospitalised for "a crisis of nerves" after learning of the alleged affair a day before Closer hit news stands.

Citing journalist friends of Trierweiler who have been in touch with her, Europe 1 radio described the former Paris Match political reporter as being in a state of nervous exhaustion characterised by extreme mood swings.

The usually reliable station also reported that she was preoccupied with the idea that "enemies" at the presidential Elysee Palace must have conspired to ensure Hollande's affair became public with the aim of forcing her out.

Lawsuit filed

Paris Match, which employed Trierweiler as a political reporter and for whom she still writes a literary column, depicted a relationship in its death throes.

The weekly described how Trierweiler became isolated and lonely as Hollande grappled with the pressures of office, which have been exacerbated by a stagnant economy and his plummeting approval ratings.

"Slowly the spiral of the nation's problems swallowed up the couple's intimacy," Paris Match reported.

In another development, a Closer representative said on Thursday that Gayet had filed a case against the magazine for alleged invasion of privacy over its report.

The magazine has received legal documents laying out the suit which seeks 54,000 euros ($74,000) in damages and other fees, plus the publication of a summary of any judicial ruling in the case on its front page.

The representative, who spoke on condition of anonymity because she was not authorised to publicly discuss the matter, declined to comment further.

Closer has promised another series of pictures and fresh revelations about the affair in a new edition on Friday.

Source: Agencies