It is unlikely that Sharon will return to office.
Vice Premier Ehud Olmert was named acting prime minister and convened the Cabinet for a special session.
A brain scan after surgery showed that the bleeding had been stopped, and the 77-year-old Sharon was transferred to the intensive care unit, said Dr. Shlomo Mor-Yosef, the director of Hadassah Hospital in Jerusalem.
"The situation is still serious, but it's stable," Mor-Yosef said. "All the parameters ... are as expected following this type of surgery. Part of the treatment of the prime minister, in order to preserve low pressure in the skull, is sedation and respiration for at least the next 24 hours."
Mor-Yosef also addressed rumors sweeping the country that Sharon's condition is far worse than described by his doctors. "I came here first to update you and second to stop the rumors that are flooding the country," he said. "I pledge that every change in the prime minister's condition will be announced in a statement by Hadassah."
Sharon's stroke threw Israeli politics and diplomacy throughout the region into turmoil amid election campaigns for both Israel and the Palestinians.
Israeli elections will be held as scheduled March 28 despite Prime Minister Ariel Sharon's grave illness, Attorney General Meni Mazuz said Thursday.
Palestinian officials said they feared the Israeli prime minister's massive stroke could disrupt Palestinian parliamentary elections Jan. 25.
U.S. envoys were to meet with Sharon Thursday evening, apparently to urge Israel to reverse a decision to ban Palestinian voting in disputed Jerusalem. But Palestinians said that the Americans had postponed their trip to the region because of Sharon's illness.
Palestinian leader Mahmoud Abbas has said he may not hold elections if Jerusalem, claimed by the Palestinians as a capital, is excluded.
"Sharon did win some respect from Palestinians because he pulled Israel out of the Gaza Strip, he dismantled 25 settlements — that's something no Israeli leader has ever done — so some Palestinians feel that Sharon was a man with whom they might be able to do business," reports CBS News correspondent Robert Berger. "Others, especially militants, felt that Sharon was a dictator and a war criminal."
"We are looking all the time for a leader in Israel to be in favor of peace and ready to sit with Palestinians to start very serious and credible negotiations," Palestinian Prime Minister Ahmed Qureia said. "No doubt, this is an event that will have implications not only for Israel, but the entire region."
Sharon had been expected to easily win re-election in March at the head of the moderate Kadima Party he created to free his hands for further peace moves with the Palestinians.
Many Israelis see Sharon — an overweight war hero and longtime hawk who changed tack and withdrew from the Gaza Strip last year — as the best hope for achieving a peace deal with the Palestinians. His illness would create a power vacuum in the government and cloud the electoral prospects of his party, which was built around Sharon.