The reported improvement came a day after Sharon slightly moved his right arm and leg in response to pain stimulation and started breathing on his own. Sharon, 77, remained hooked up to a respirator and unconscious in a guarded room where classical music, including Mozart, is being played.
Israelis were breathing a collective sigh of relief now that doctors say Sharon has a good chance to survive, reports CBS News correspondent Robert Berger, but they're concerned that Sharon may be paralyzed and his ability to think may be impaired. It's hard for Israelis to come to terms with the tough former general and war hero and energetic prime minister confined to a wheelchair.
Also, an Israeli newspaper reported that Sharon was suffering from a brain disease that, in combination with the blood thinners he started taking after an initial stroke Dec. 18, could have increased his risk for another stroke. Doctors refused to comment.
Doctors said it would be days before they could assess the damage to Sharon's brain from the cerebral hemorrhage he suffered Wednesday. A final medical analysis on Sharon's long-term prognosis would end days of uncertainty over the fate of the prime minister, heralded by many as the best hope for Mideast peace.
On that front, Israel's defense minister said Israel will permit Arabs in Jerusalem to vote in Palestinian elections scheduled for Jan. 25. The decision appeared to resolve a standoff that had threatened to derail the balloting and heighten frictions between Israel and the Palestinians at this sensitive time.
The issue was widely seen as a key test for acting Prime Minister Ehud Olmert.
Polls show that the 60-year-old Olmert has a good chance to win elections in March.
"He's been in politics an awfully long time, he's been in Knesset (parliament) for a long time, he's a lawyer by training, he's very smart and savvy," said Jerusalem Post editor David Horovitz.
But Berger points out Olmert will be facing with another smart and savvy politician, former prime minister Benjamin Netanyahu. What Olmert has going for him is that he is the right-hand man of the popular Sharon.
Olmert's first diplomatic test as acting prime minister was whether to let Palestinians vote in east Jerusalem in parliamentary elections.
Israel had been threatening to prevent voting in Jerusalem because it was reluctant to be seen as granting any kind of legitimacy to the Islamic group Hamas, which is committed to Israel's destruction and is running in the balloting.
But on Tuesday, Israeli Defense Minister Shaul Mofaz said Arab residents of Jerusalem could vote.
"I think the policy of the state of Israel still stands," Mofaz told reporters in Jerusalem. "There will be elections in east Jerusalem."
Because of the city's symbolic importance, Palestinian leader Mahmoud Abbas had threatened to call off the elections if Israel banned east Jerusalem voting.
Sharon's doctors put him in a coma to give him time to heal from the recent stroke and three subsequent brain operations. They began weaning Sharon from the sedatives Monday. Despite Sharon's reported movement, doctors doubt he will recover enough to resume his duties because the bleeding in his brain was extensive.
Movement on Sharon's left side could be very significant because that part of the body is controlled by the right side of the brain, where Sharon's stroke occurred.
Dr. Anthony Rudd, a stroke specialist at St. Thomas' Hospital in London, called the reports "surprising."
"It's certainly better than what I would have predicted so far. Based on the fact that he had a large hemorrhage in the right side of the brain I would have predicted advanced paralysis," Rudd said.
However, he said it was possible the movement was simply involuntary reflexes.
"It doesn't take us terribly far forward," he said. "There is still a significant risk of dying."
Sharon's doctors, however, say there is no immediate threat to Sharon's life.
Meanwhile, the Haaretz daily said Sharon was suffering from a brain disease called cerebral amyloid angiopathy. If doctors had known about the condition earlier, they would not have prescribed the blood thinners, the paper said, quoting an unidentified member of Sharon's medical team.
Rudd said the condition is a common cause of bleeding in the brain, particularly in the elderly, but hard to diagnose without a biopsy.
"This protein, amyloid ... is deposited in the walls of the arteries, and it makes the walls of the arteries much more fragile and liable to rupture," he said. "And very often, there is a high risk of recurrent bleeding."
He said the blood thinners would not have caused the hemorrhage but would worsen the bleeding.
Sharon was given the blood thinners after his mild stroke last month, but the brain condition was discovered only after the second stroke, Haaretz said.
Hospital spokeswoman Yael Bossem-Levy declined to comment on the report.
"We are busy treating the prime minister and fighting for his life and nothing else," she said.