The statement from Jerusalem's Hadassah Hospital said Sharon's condition, unchanged overnight, is critical but stable. Doctors began removing anesthetics on Monday, and say the Israeli leader has responded to pain stimuli with slight movements of his right leg and arm.
Sharon remains hooked up to a respirator and unconscious, in a guarded room where classical music is being played.
Sharon, 77, has been in a medically-induced coma since his stroke, a state doctors felt would give him a better chance to heal. Doctors Monday began the process of bringing him out of the coma, by gradually reducing the amount of sedatives in his system, and Sharon responded by breathing on his own, and later, with the arm and leg movements.
Sharon's chief surgeon said the leader's response to pain stimulation is "very important" but it is too early to assess Sharon's ability to think and reason. It will take several days for all the sedatives to be withdrawn.
By Monday afternoon, Sharon had begun breathing on his own, though he is still on a respirator to assist him, said Dr. Shlomo Mor-Yosef, director of Hadassah Hospital, where Sharon is being treated.
Dr. Felix Umansky, the chief neurosurgeon treating Sharon, said doctors hoped that as the sedatives are further decreased that Sharon will have a greater response to pain stimulation, including opening his eyes.
"Once he talks to us ... and there are no other infections I will be willing to say that he is completely out of danger," Umansky said.
Israel's Ynet Web site quoted Sharon aides as saying. "The situation is much better than before. We're happy about the good signs."
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.
Although it is too early to know for sure, medical experts say it is likely that Sharon suffered some brain damage and paralysis.
Doctors will pass their assessment of Sharon's medical condition to Attorney General Meni Mazuz, who will 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.
Sharon, Israel's most popular politician, was seen by many here as the best hope for resolving the Israel-Palestinian conflict. His abrupt illness and expected departure from the Mideast political stage has raised concern that momentum on territorial concessions, created by his recent Gaza Strip withdrawal, would stop, and that Sharon's successor wouldn't have the stature to forge ahead on drawing Israel's final borders.
In the event the attorney general declares permanent incapacitation, the Cabinet would have to elect a new prime minister within 24 hours, from among the five sitting Cabinet ministers from Sharon's Kadima Party who are also lawmakers, Galanti said.
That group includes Olmert, a potential political heir.
Before his collapse, Sharon appeared headed to a landslide victory in March 28 elections at the head of the Kadima Party, which seeks further pullbacks while strengthening Israel's hold over major settlement blocs.
Olmert told the Cabinet on Sunday that he would work to carry on Sharon's political legacy.
Doctors not involved in Sharon's care said that if he awakens, the extent of his responses could vary widely, from slight movements of the fingers or opening of the eyes, to a much fuller awakening. They have also cautioned that there is no guarantee that Sharon will awaken from the anesthesia.
That Sharon can breathe on his own "tells us that one part of his brain is functioning, the respiratory center," said Dr. John Martin, a professor of cardiovascular medicine at University College in London. "It doesn't tell us how he is thinking, it doesn't tell us how he can speak, it doesn't tell us how he can move his arms and legs.
"His chances of survival are better than if the respiratory center had been damaged, but that still doesn't mean he's going to survive. ... It is still highly probable that he will die," Martin added, noting that Sharon's weight and age work against him.
One of Sharon's surgeons, Dr. Jose Cohen, said that while Sharon's chances of survival were high, his ability to think and reason would be impaired.
"He will not continue to be prime minister, but maybe he will be able to understand and to speak," Cohen said in comments published Sunday by The Jerusalem Post.
Israel's Cabinet met for its weekly gathering Sunday for the first time since Sharon's stroke.
Olmert, sitting next to Sharon's empty chair, promised to "carry out the wishes of Sharon."