Former Formula one champion Michael Schumacher has undergone a second operation to treat brain injuries sustained in an off-piste skiing accident, as his doctors said they had seen a “slight improvement” in his condition.

In a press conference at the university hospital in Grenoble where the seven-times world champion was airlifted on Sunday, doctors said they had decided, in conjunction with the Schumacher family, to carry out more surgery following a modest improvement in his condition and a brain scan yesterday afternoon.

The medical update came as the prosecutor’s office in the Alpine resort town of Albertville, which is overseeing the investigation into Schumacher’s accident, confirmed that his helmet had split in two when he fell.

“It broke apart in two pieces,” an official from the prosecutor’s office said. However, the official added that was too early to infer that the helmet had broken because of the high speed at which Schumacher was skiing downhill.

“It’s too early to draw conclusions about excessive speed,” said the official. “It will take two or three more days to know exactly what happened.”

During the operation, which began at 10pm and lasted two hours, a haematoma was removed from Schumacher’s brain and the intracranial pressure further decreased.

A fresh scan carried out this morning had confirmed “signs ... of slight improvement,” said Jacqueline Hubert, director of the hospital.

But the doctors warned that the driver’s condition remained critical, with more bruising and more lesions that have yet to be treated. He remains in a medically induced coma following the accident in which he fell and hit his head on rocks in the ski resort of Meribel.

“The situation is better controlled than yesterday,” said chief anaesthesiologist Jean-Francois Payen. “We cannot say he’s out of danger but today... we have bought a bit of time.”

The decision to go ahead with the operation had been taken in conjunction with the Schumacher family. His wife, Corinna, two children and brother are all at the hospital with him, said Gerard Vaillaint, a leading brain surgeon and friend of the German driver.

Vaillaint, with the Grenoble medical team, refused to enter into prognostics and said any attempt to predict Schumacher’s future, even over the next few days, was pointless.

“We cannot say it’s over. We can say there are highs and lows ... but it’s a bit better than it was yesterday,” said Emmanuel Gay, chief of neurology at the hospital.

Gay said the medical team had been “a bit surprised” by their patient’s modest improvement. “But, careful,” he added, “there is still a long way to go.”

Schumacher (44), has been in the hospital in the eastern French city since Sunday at 12.40pm, when he was airlifted from a smaller hospital in the Alpine town of Moutiers. He had been skiing down an unmarked slope near Meribel with his 14-year-old son when he fell and hit his head.

Doctors treating Schumacher in Grenoble were asked about the helmet at a news conference earlier today. One said that the driver had a scar on his head which had affected the cranial bone, but did not confirm that it was caused by the helmet shattering. The former champion’s skis are also being analysed by experts.

Yesterday, the doctors treating him said his condition was “life-threatening” and that they were working on an “hour by hour” basis to save him. Today, despite the signs of improvement and a second successful operation, they insisted it would be premature to say the battle was over. The scan had revealed multiple haematoma on Schumacher’s brain. The second operation had been carried out to remove one of them which, on the left of the brain, was accessible and removal of it did not present large risks.

For the moment, the doctors said, there was no question of Schumacher being woken from the medically induced coma, which is designed to ease the swelling on his brain.

Equally, added Payen, there was no immediate possibility of his being transferred to another hospital nearer to home.

The gravity of the retired champion’s condition has prompted figures from across the sporting world to express their shock at the accident and solidarity with a man regarded as one of the greatest racing drivers in Formula One’s history.

The current world champion and fellow German Sebastian Vettel, who has been dubbed “Baby Schumi” by his country’s media, led a chorus of support and concern from the sport. “I am shocked and hope that he gets better as quickly as possible. I wish his family much strength,” he said.

The British driver Jenson Button, another former world champion, said: “My thoughts are with Michael Schumacher at this tough time. Michael more than anyone has the strength to pull through this.”

Angela Merkel, the German chancellor, said she was “extremely shocked along with millions of Germans”.

Schumacher is thought to have been skiing downhill between two marked pistes below the jagged peaks of the Dent de Burgin when he fell, hitting the right side of his head.

Investigators from the Gendarmerie based in the resort of Bourg St Maurice were on the mountainside yesterday attempting to establish the exact circumstances of the accident, which occurred at 2,100m.