Shlomo Mor-Yosef, the director of Hadassah hospital in Jerusalem, said on Monday: "The prime minister started immediately to breathe on his own but he's still hooked up to a respirator."
Yael Bossam-Levy, a spokeswoman for the hospital, said: "The consultations of the doctors have finished. The progressive awakening of the prime minister has begun."
The expected decision to go ahead with the procedure followed a further round of consultations between Sharon's medical team on Monday morning.
Doctors have said that the procedure is critical for determining the extent to which Sharon's faculties have been impaired and his chances for survival.
Sharon, 77, has been treated at Hadassah since he suffered a brain haemorrhage on Wednesday night.
Shlomo Mor-Yosef, the director at Hadassah, said of the awakening procedure on Sunday: "This is what we have all been waiting for since Wednesday - to see how the prime minister's brain is functioning."
Sharon's surgeons say there is a good chance he will live. But medical consensus is he has suffered too much damage to ever return to politics.
If doctors determine that Sharon is permanently incapacitated, they will pass on their finding to Israel's attorney-general. The cabinet would then choose a new prime minister from ministers of Sharon's new centrist Kadima party.
Ehud Olmert, Sharon's deputy, has taken over as acting prime minister, and is expected to keep the position in the run-up to a general election scheduled for 28 March.