"The clinical state of Michael Schumacher is stable as he's under permanent care and treatment," Grenoble hospital said in a statement on Monday.
"However, the medical team in charge stresses that it continues to assess his situation as critical."
The statement appears to be at least in part a response to comments made by a friend of Schumacher at the end of last week, the former F1 driver Philippe Sttreiff, who said that "Michael's life is not in danger any more" based on something told him by a mutual friend of his and Schumacher's, Dr Gerard Saillant.
Schumacher's agent Sabine Kehm spoke out when asked about after Sttreiff's comments, reinforcing that the seven-times world champion was still in a critical condition.The medical team and the German's management repeated on Monday their call to respect his privacy and said they would not send any more statements nor hold any news conference until further notice.
Last week his agent Sabine Kehm urged journalists to stay away from Schumacher after security guards said they intercepted a reporter disguised as a priest who was trying to get into his room.
"The patient's privacy requires that we do not disclose any details about his treatment and that's why we do not plan any news conference nor written statements for now," said the medical team and Schumacher's management.
"We ask you again, insistently, to stick to the information provided by the medical team in charge or his management because they are the only valid ones."
While Schumacher is battling for his life after suffering severe internal bleeding on the skull, French authorities are investigating the accident that took place in the Alps resort of Meribel.
The Annecy prosecutor on Monday said he will hold a news conference on Wednesday.