Doctors say Ariel Sharon has moved his eyelids, 12 days after suffering a huge stroke, but he still remains in a coma.
Israel's attention has been focused on developments at Hadassah
Israeli media said the prime minister opened his eyes and seemed to recognise people around his bed, but this has been denied by Hadassah Hospital.
"He blinked both eyes but the medical significance of this is not clear," a hospital spokeswoman said.
Israelis have been closely following Mr Sharon's treatment, hoping that the veteran leader will recover.
On Sunday, doctors gave Mr Sharon a tracheotomy, a procedure in which a small hole was cut into his neck so that he could be taken off a respirator.
Hadassah Hospital spokeswoman Maho Stainberg described the reports of Mr Sharon opening his eyes as "not true".
A hospital statement said that family members had interpreted "eyelid movements" as an opening of Mr Sharon's eyes.
ARIEL SHARON'S HEALTH
Sharon suffers minor stroke on 18 December 2005
Doctors discover small hole in heart, schedule operation for 5 January
Sharon rushed to hospital one day before scheduled surgery with major stroke
Undergoes two operations overnight on 4/5 January, followed by third on 6 January
But another report, quoting a doctor who is treating Mr Sharon, seemed to paint a more positive picture.
"He was listening to a tape of his grandson and you could see tears in his eyes for a matter of seconds before he closed them again," the doctor told AFP news agency on condition of anonymity.
A medical source said that Mr Sharon's son Gilad was in the room at the time.
Hospital officials say it is too early to tell whether the development represented a significant improvement or was just a temporary reflex.
Tests have shown activity on both sides of Mr Sharon's brain. His condition is said to be serious but stable.
A new brain scan on Sunday showed no change in his condition.
Spokesman Ron Krumer has said it could take days or even weeks for Mr Sharon to wake up, and that doctors were not standing over him with a stopwatch.
The 77-year-old leader suffered a major stroke on 4 January and has remained in a coma following three operations to stem bleeding in his brain.
As Mr Sharon's coma drags on, Israelis are resigning themselves to the idea of a political future without him.
Israel's Attorney General Menachem Mazuz released a statement on Sunday saying that should Mr Sharon's condition persist, he cannot under Israeli law be declared permanently incapacitated for another three months.
He directed Mr Sharon's replacement, Ehud Olmert, to stay on as acting prime minister until Israel goes to the polls on 28 March.
On Monday Mr Olmert was also declared acting chairman of the centrist Kadima party which Mr Sharon created last year after his right-wing Likud split over the withdrawal from Gaza.