The medical director of the AEK hospital in central Budapest, which is renowned as one of the best neurological units in Europe, created alarm overnight when he said the Ferrari driver's injuries were "life-threatening".
Ferrari and formula one officials insisted that prognosis was alarmist, but Peter Bazso repeated his concern on Sunday, having awakened 28-year-old Massa briefly to conduct further tests.
While Massa's coma was briefly interrupted, it is said that he recognized his family and attempted to speak.
But when asked if the Brazilian's life is still in danger, Bazso answered: "Yes, of course.
"He is in an acute phase. What can come next, we don't know."
He revealed that Saturday's surgery was to remove broken bones in his skull, but said Massa had so far responded as expected from the injuries sustained.
Bazso refused to respond to speculation that Massa may be sidelined for the rest of the 2009 season, or that there may be permanent damage.
"At the moment, we have to overcome this life-threatening condition," he insisted.
Ferrari's team boss Stefano Domenicali visited the hospital on Saturday as well as on Sunday morning, and told reporters at the Hungaroring that he would return after the race.
His race engineer Rob Smedley has also been at the AEK hospital, where his wife and parents are at Massa's bedside having flown in overnight from Sao Paulo.