Mr Sharon has been transferred to the intensive care unit and doctors say his vital signs are stable.
But he remains in surgery in a "serious" condition, according a spokesman from Jerusalem's Hadassah hospital.
Shlomo Moryussef said Mr Sharon underwent a CT scan that showed the cerebral haemorrhaging has stopped.
Earlier, Mr Sharon had to be readmitted to surgery after undergoing an initial six-hour operation to stem bleeding in his brain.
"The prime minister has been taken back to the operating theatre and we are now continuing the same operation as there are additional areas that have to be treated," said the hospital director, who also described the leader's condition as "serious".
His prime ministerial powers have been transferred to Finance Minister Ehud Olmert.
Mr Sharon's spokesman Ranaan Gissin said the operation to drain blood from Mr Sharon’s brain went well, but described his condition as "much more serious" than his previous stroke.
But doctors said a stroke of this magnitude would have caused extensive damage.
Serious condition
Mr Sharon, 77, suffered a minor stroke in December, however was back at work within a day.
His admittance to hospital came hours before he was due to undergo a procedure to repair a small hole in his heart to prevent a repeat of his previous stroke.
Medical experts said the operation is potentially life-threatening, and even if he does survive, he can expect to remain incapacitated for some time.
A neurologist told CNN that even if he does survive, he will be in a coma or remain in a stupor for days.
"We would be looking at weeks, if not months, before he would be functioning close to normally," he said.
Mr Sharon was at his ranch in the southern Negev desert on Wednesday when he suddenly "felt ill", a close aide said, and was admitted to hospital just before 11pm local time.
Uncertainty
Mr Sharon's stroke has plunged Israel into political uncertainty, less than three months before a pivotal election.
The leader, who turns 78 last month, has already announced his intention to seek a full term if re-elected for the third time in a March 28 poll.
If successful, he would lead until the age of 82, which would make him Israel's oldest ever leader.
While he has cut down on his foreign travels in recent years, he still maintains a punishing workload.
Mr Sharon has been under huge stress in recent weeks: his son Omri is facing prison after pleading guilty to charges of providing false testimony and falsifying documents following an investigation into allegations of illegal financing of one of his father's leadership campaigns.
Reports also emerged on Tuesday night that Israeli police are to examine computer data which they believe will show Mr Sharon's family received an alleged US$3 million bribe from Austrian financier Martin Schlaff.
Mr Sharon and Kadima have been riding high in the opinion polls, forecast to emerge as much the largest party after the election.
However, although Mr Sharon has been able to attract other heavyweights such as Ehud Olmert, his new party is seen as largely a one-man band with few concrete policies or party institutions.
The issue of a prime minister's health at election time has become sensitive in Israel after two of Mr Sharon's late predecessors, Golda Meir and Menachem Begin, both concealed major health problems from voters.