On Saturday medics said they had detected a reduction in the swelling in Sharon's brain, after three bouts of surgery to stem bleeding after the premier suffered his second stroke in about two weeks on Wednesday.
But they said they would be able to assess the extent of the damage caused to Sharon's brain only after they had woken him from a medically induced coma. A decision about when to wake him was due on Sunday morning.
One neurosurgeon said he thought that Sharon, 77, would recover from the massive stroke and emerge in relatively good shape, but that after such a shock there would undoubtedly be cognitive damage.
Israelis and world leaders have already braced themselves for the end of the Sharon era, fearing that his demise would spark new turmoil in the region.
Even if he were to pull through, few people believe that Sharon will be in any condition to return to the helm of his new Kadima party and contend a general election in March.
Signs of improvement
In a bulletin issued to reporters late on Saturday, medics said the latest brain scan had shown signs of improvement and that all his other "vital signs were within normal limits".
"He has survived several wars and he is fighting once more for his life. It's a question of faith"
But Shlomo Mor-Yosef, director of Hadassah hospital in Jerusalem, said the prime minister remained "still critical and stable".
Cohen, one of the neurosurgeons treating Sharon, was quoted by Israeli radio as saying: "The prime minister has a solid constitution. He will stay alive and will be in relatively good shape."
Ranaan Gissin, Sharon's chief spokesman, also said he expected the prime minister to pull through but said that only the doctors could say whether he could ever resume his duties.
"He has survived several wars and he is fighting once more for his life. It's a question of faith," he told AFP.
Sharon, who has been premier since early 2001, and his new centrist Kadima party had until a few days ago seemed a shoo-in for a general election set for 28 March but all previous calculations are now being revised.
Jack Straw, the British foreign secretary, said that Israel faced a period of great uncertainty while Sharon fought for his life.
But even if Sharon had been well, there would have been little movement on the political level "until the end of March and the formation of a new government", he said.
King Abdullah II of Jordan said he hoped that the Middle East peace process would not be affected by Sharon's illness, in a phone call to Ehud Olmert, the acting prime minister, a palace official said.
Before Israel goes to the polls, the Palestinians are also scheduled to elect their own new government on 25 January.
Mahmoud Abbas, the Palestinian leader, has said that Sharon's illness should have no impact on the ballot, but he has also threatened to postpone it if Israel does not guarantee that voting can take place in occupied east Jerusalem.