Sharon showed "significant improvement" after five hours of emergency brain surgery on Friday, but he is still in serious condition and doctors said he would be kept in a medically induced coma for at least two more days.
Sharon's chief surgeon said it was too early to assess the damage the prime minister suffered after two surgeries to stop brain hemorrhaging in as many days, but independent medical experts said the prime minister's prognosis appeared dire.
Sharon's aides held a grim vigil at the hospital and Israeli elder statesmen Shimon Peres said he is "very worried" about his old friend.
Sharon's illness froze politics across the region, and its repercussions were felt around the world. U.S. Secretary of State Condoleezza Rice canceled a six-day trip to Indonesia and Australia because of Sharon's struggle to survive.
Rice called acting Prime Minister Ehud Olmert on Friday. "Every U.S. citizen, from the President to the last citizen are praying for Sharon's health," Rice said, according to Olmert's office.
"Despite the difficult situation, this evening Israeli citizens have a little more hope," Olmert told her.
Egyptian President Hosni Mubarak also called Olmert on Friday to wish Sharon a speedy recovery, said Olmert's spokeswoman, Haya Perry.
Sharon's sons, Omri and Gilad, were camped out in a room next door to their father's at the neurological intensive care unit. Sephardic Chief Rabbi Shlomo Amar took to the airwaves to advise Israelis which psalms to read for Sharon. "All that is left to do is to pray," Israel's other chief rabbi, Yona Metzger, said.
Shmuel Rabinovitch, rabbi of the Western Wall, said he received dozens of e-mails praying for Sharon's health that he printed out and stuck in the cracks of the holy site. Callers from as far away as Venezuela and the United States asked for advice in praying for Sharon, he said.
Sharon was rushed into the operating room Friday morning after a brain scan indicated rising cranial pressure and further brain hemorrhaging.
Hadassah Hospital director Dr. Shlomo Mor-Yosef said the new surgery Friday helped stabilize Sharon's condition. "Part of the blood clots that remained after the first operation were drained," he said. "At the end of the operation, there is no active bleeding and the intracranial pressure has returned to normal."
Mor-Yosef said a comparison of brain scans before and after the surgery showed "significant improvement," but he did not elaborate.
The chief neurosurgeon operating on Sharon, Dr. Felix Umansky, said he came through the surgery well, but was likely to have suffered damage.
"There is always some damage when you have cerebral hemorrhage," he said in a telephone interview. "We cannot assess the damage because he is under anesthesia all the time. We need to wait and see what will happen once we reduce the medication which keeps him under sedation."
Hospital officials said Sharon would remain in a medically induced coma until at least noon Sunday to give him time to heal.
The surgery Friday followed a seven-hour operation Sharon underwent Thursday after he suffered a massive brain hemorrhage as he rode in an ambulance to the hospital from his ranch in southern Israel.
Sharon's illness threw Israeli politics into flux less than three months before national elections. Israeli officials said the elections would proceed as scheduled regardless of Sharon's fate.
Leaders of Sharon's new Kadima Party said they would rally around Olmert.
A new poll released Friday showed the party would still sweep the vote, even without Sharon, who formed the centrist party after bolting the hardline Likud last year following his withdrawal from the Gaza Strip.
The poll published in the Yediot Ahronot daily Friday found that an Olmert-headed Kadima would win 39 of 120 parliament seats, slightly less than the party polled under Sharon, but enough to lead the next government.
The poll of 500 people was taken Thursday and had a margin of error of 4.4 percentage points. Some pollsters said the results might be influenced by sympathy for Sharon, and could change during the campaign.
The poll showed Peres would net 42 seats as Kadima leader, but analysts said it was unlikely he would be chosen to lead the party. Peres met with Olmert on Friday, but did not give details of their talk.
"We will know how to continue Israel's policy ... to continue Ariel Sharon's policies," Peres said.
Palestinian leaders, holding a parliamentary election of their own Jan. 25, said they were in touch with Israeli officials about Sharon's condition. "We are closely monitoring the situation," Palestinian negotiator Saeb Erekat said.
The White House declined to speculate on how Sharon's illness could affect the peace process.
"The United States view of the Middle East is that the desire for progress and peace runs wide and deep," spokesman Trent Duffy said. "The president continues to pray for the recovery of Prime Minister Sharon."
Israelis expressed concern for Sharon as they rushed to prepare for the coming of the Sabbath on Friday. Some worried that Sharon was not coming back.
"It's very sad that he's going, he was a real leader, from the establishment of the state until now," said Itzik Gordon, a 48-year-old contractor.
Sharon rose to prominence as a legendary army officer, and later entered politics in Likud. As defense minister, Sharon directed Israel's ill-fated invasion of Lebanon in 1982 and was forced to step down after being found indirectly responsible for a massacre of Palestinian refugees by Christian Phalangist soldiers.
He re-emerged as prime minister in 2001 after the outbreak of new Israeli-Palestinian violence, and four years later he reversed his long support for Jewish settlement and pulled Israel out of Gaza.