The death has thrown Israel into political turmoil, barely three months before a general election.
Doctors said there was no change in his condition overnight, and he remains on a life support machine more than 24 hours after the end of an operation to stem bleeding in his brain.
"There has been no change during the night. All the vital signs that we
measure -- blood pressure, intra-cranial pressure -- all these vital signs have
been stable, within the normal levels and this is positive," said Shlomo Moryussef, director of the Hadassah hospital in Jerusalem where Mr Sharon was taken after suffering the stroke.
Doctors will meet later on Friday to discuss whether the 77-year-old leader should undergo another CT scan.
Mr Sharon could remain in the induced coma for several days, and it could be a week before doctors know whether he suffered any permanent damage.
Mr Sharon was admitted to hospital late on Wednesday night, just hours before he was due to undergo a routine procedure to repair a small hole in his heart to prevent a repeat of a minor stroke he suffered on December 18.
"Mr Sharon is under sedation, anaesthesia and ventilation. The purpose is to reduce the intra-cranial pressure in the prime minister's brain," Mr Moryussef said earlier.
"This will last 48 to 72 hours, it depends on his condition. Then gradually we will try to awake the prime minister in order to see his response and brain activities."
But many analysts say it is unlikely Mr Sharon will return to politics.
His deteriorating health came as he was seeking election to a third term in office as head of his new centrist Kadima party.
Officials say the scheduled March 28 poll will go ahead as planned.
Grave fears
As Mr Sharon's sons Omri and Gilad gathered at their father's bedside, some of the premier's closest allies said his life remains in danger and acknowledged that the man who has made an indelible mark on Israel's political and military landscape is unlikely ever to be able to return to office.
Two of Mr Sharon's closest allies, Transport Minister Meir Sheetrit and the leader in parliament of his newly formed Kadima party, Ronni Bar-On, both confirmed the gravity of the situation by saying the prime minister was “fighting for his life".
Haim Ramon, an MP who joined Kadima from the centre-left Labor party, acknowledged that Mr Sharon was unlikely to return to work.
"I pray that he will recover, but it seems to me that he will not be able to exercise his functions as prime minister any time soon or perhaps ever."
Prime Ministerial powers have been transferred in the short term to Finance Minister and Deputy Prime Minister Ehud Olmert.
Mr Sharon’s exit from politics would not only be a blow to Kadima's chances but could also revive the prospects of Likud, led by Sharon's hawkish rival Benjamin Netanyahu.
US President George W Bush sent his prayers for "a man of courage and peace" while Secretary of State Condoleezza Rice called Mr Sharon a "huge and gigantic figure in Israeli politics."
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.
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 that Israeli police are to examine computer data they believe will show Mr Sharon's family received an alleged US$3 million bribe from Austrian financier Martin Schlaff.