The process was expected to take six to eight hours, reports CBS News correspondent Robert Berger. The doctors then will conduct tests to see how Sharon responds.
Israel's Channel 10 reported that Sharon moved one of his hands as doctors roused him. "He coughed and moved," the Ynet Web site quotes Sharon aides as saying. "The situation is much better than before. We're happy about the good signs."
Outside experts said that while independent breathing meant Sharon had better chances for survival, it gave no indication about his other physical or mental capacities.
Doctors made the decision to lift the anesthesia after a round of consultations Monday. Hospital director Dr. Shlomo Mor-Yosef said the process of weaning Sharon from sedation could take hours or days.
"As soon as we started reducing the drugs ... the prime minister started to breathe independently, although he is still hooked up to a respirator that is used as an aid," Mor-Yosef said. He added that Sharon remains in critical condition.
Sharon suffered a severe stroke on Wednesday, two weeks after a first, mild stroke, and was rushed to Hadassah where he has undergone two surgeries to stop bleeding in his brain.
Doctors have kept him in a medically induced coma and on a respirator since Thursday to give him time to heal from the trauma of the stroke and the surgeries.
After withdrawing the sedatives, doctors were to pass their assessment of brain damage to Attorney General Meni Mazuz, who will then decide whether to declare the prime minister permanently incapacitated.
"The minute we know what damage has occurred, we will talk," Justice Ministry spokesman Yaakov Galanti said.
Since an acting prime minister is in place, there is no urgency to such a declaration, Galanti added.
Ehud Olmert, Sharon's deputy, has been named acting prime minister and can serve in that role for 100 days.
Outside experts have said doctors should have a good idea of the extent of the damage by the end of the day. One of Sharon's neurosurgeons has cautioned that it was unlikely he could function as prime minister again.
"My guess is he'll be in the ICU and on a respirator for quite some time," Dr. Keith Siller, head of neurology at New York University Medical Center, told CBS News' Tony Guida.
Because he is a head of state, it would have been inconceivable for doctors not to attempt every intervention, but Siller said that might not be best for Sharon.