JERUSALEM (AP) – Doctors reported progress Tuesday by Ariel Sharon, saying the Israeli leader moved his left hand and appeared to respond to his sons’ voices in new signs of recovery from a massive stroke.

But while doctors said Sharon was no longer in immediate danger, they cautioned it would be days before they could determine the full extent of the damage he suffered from a brain hemorrhage and whether he has lost his ability to think and reason.

“I think compared with recent days … there are significant changes in the prime minister’s condition. But we still have a long way to go, and we have to be patient,” said Dr. Yoram Weiss, one of Sharon’s anesthesiologists.

Sharon suffered a massive stroke Jan. 4 and underwent three surgeries to stop hemorrhaging on the right side of his brain. He has been kept in a medically induced coma to give him time to recover.

Israelis were stunned at the illness of their 77-year-old leader and have intensely followed updates on his condition. Some made pilgrimages to Hadassah Hospital, gathering outside to pray, hanging up posters of support and offering letters of well wishes, many written by children.

Israeli police said crime in the country had fallen 50 percent since Sharon’s stroke. “It’s hard to explain, but since the prime minister became ill there seems to have been a change in people’s behavior patterns, their way of thinking,” police spokesman Mickey Rosenfeld said.

In his first public statement since his father’s stroke, Sharon’s son Omri said the family was grateful for the outpouring of support.

“I came to thank, in the name of my family, the citizens of Israel, who since Wednesday have supported us with their concern, with warm and loving prayers for the well-being of my father,” he told reporters outside the hospital. “In addition, I want to send our great appreciation and thanks to Hadassah Hospital, the medical team treating my father and his personal doctors who have been working day and night to treat the prime minister.”

Also Tuesday, Secretary of State Condoleezza Rice called acting Prime Minister Ehud Olmert to check on Sharon and renew the Bush administration’s support for establishment of a Palestinian state.

Sharon suffered an initial, minor stroke Dec. 18, which doctors said was caused when a blood clot escaped through a small hole in his heart. Doctors prescribed blood thinners ahead of a planned procedure to close the hole. Outside experts said the blood thinners could have worsened Sharon’s brain hemorrhage.

Mor-Yosef said Tuesday that doctors had discovered after Sharon’s initial stroke that he suffered from cerebral amyloid angiopathy, a disease that can cause brain bleeding, particularly in the elderly. The revelation raised questions about the doctors’ decision to prescribe blood thinners.

Dr. Anthony Rudd, a stroke specialist at St. Thomas’ Hospital in London, said giving blood thinners to a person suffering from the brain disease “certainly wouldn’t be standard procedure,” but it was a judgment call and indicated his doctors believed the hole in his heart was more of a risk than a brain hemorrhage.

“I’m sure that the decisions they made were made in good faith based on the information they had,” he said.

On Monday, doctors began decreasing the sedatives that have kept Sharon in a coma, and he started breathing on his own and moved his right arm and leg slightly in response to stimulation. On Tuesday, he increased his movement on the right side and also moved his left arm in response to stimulation, said Dr. Shlomo Mor-Yosef, the director of Hadassah Hospital.

Movement on Sharon’s left side could be significant because that part of the body is controlled by the right side of the brain, where Sharon’s stroke occurred.

Rudd called the news “surprising.”

“It’s certainly better than what I would have predicted so far. Based on the fact that he had a large hemorrhage in the right side of the brain, I would have predicted advanced paralysis,” he said.

Sharon’s sons were playing Mozart as well as one of his favorite Israeli songs, “The King’s Bride,” by folk singer Rivka Zohar, in his hospital room in hopes it would elicit a further response.

Sharon remained in critical but stable condition and had a decent chance of surviving, Weiss said. “Metaphorically speaking, we have backed off five yards from the edge of the cliff,” he said.

Over the next 24 hours, the doctors will continue decreasing Sharon’s sedatives and conducting tests to further assess his brain functions. A final assessment would have to wait until the sedatives completely wear off, possibly several days, said Weiss, the anesthesiologist.

“There is improvement, but we still can’t know the extent of the cognitive improvement,” Weiss said. “We simply need patience.”

A final medical analysis of Sharon’s long-term prognosis would end uncertainty over the fate of the prime minister, heralded by many as the best hope for Mideast peace. Doctors were doubtful he would recover enough to resume his duties.

Olmert has worked hard to portray an aura of stability. His first major test is resolving the dispute over whether to allow Palestinians to vote in Jerusalem during Jan. 25 parliamentary elections.

Olmert’s office said the Cabinet would decide Sunday whether to let the city’s Arab residents cast absentee ballots in post offices provided no candidates from the militant Hamas group were on the ballot.

The campaign for Israel’s March 28 elections has been largely frozen since Sharon’s stroke. An assessment of Sharon’s condition could enable his new Kadima Party to select a successor and start campaigning. Olmert is seen as the most likely heir.