Sharon, 77, suffered a massive stroke with widespread bleeding in his brain Wednesday, and Friday's surgery was his second in two days.
Despite the improvement, Sharon is in critical but stable condition, said Hadassah Hospital director Dr. Shlomo Mor-Yosef. He said Sharon was returned to intensive care after the surgery and a brain scan.
Sharon had been rushed to the operating room Friday morning, after a brain scan indicated rising cranial pressure and bleeding.
"During surgery, the increased intracranial pressure was released, part of the blood clots that remained after the first operation were drained," he said. "At the end of the operation, there is no active bleeding and the intracranial pressure has returned to normal."
"I can say that in comparison to previous CT scans ... there is a significant improvement in the way the brain exam looks to Hadassah's experts," Mor-Yosef said.
The fact that Sharon went back into surgery is seen as a very bad sign, and is underscored by the news that several top aides left meetings to come to the hospital, reports CBS News correspondent Allen Pizzey.
Shimon Peres, Israel's elder statesman and a Sharon ally, said he was "very worried."
Sharon's sons, Omri and Gilad, were camped out in a room next door to their father's at the neurological intensive care unit.
Sharon's sudden, grave illness left his ambitious peace agenda in doubt and stunned Israelis, who were grappling with the likelihood that the man who dominated politics in the regions for decades would never return to power.
"It's a nation in mourning. The radio is playing sad songs, television is non-stop coverage," reports 60 Minutes correspondent Bob Simon. "It's mourning and it's shock, and it's very comparable to my mind to the death of [former Israeli Prime Minister Yitzhak] Rabin 10 years ago.
At Jerusalem's Western Wall, one of the holiest sites in Judaism, Orthodox Jews were praying for Sharon's recovery.
Rabbi Shmuel Rabinovitch of the Western Wall said he had received dozens of e-mails praying for Sharon's health that he printed out and stuck in the cracks of the holy site. Callers from as far away as Venezuela and the United States asked for advice in praying for Sharon, he said.
"Even if he had some things that he did that you're not happy with or disagree with, that can't change ... how he helped build the country and everything he did for the country," one Israeli told CBS News' Larry Miller.
The surgery Friday followed a seven-hour operation Sharon underwent Thursday morning after he suffered a massive brain hemorrhage. Doctors had put him in a medically induced coma to give his body time to heal, but most outside experts said his chances for recovery were slim.
Outside medical experts said bleeding from the stroke may have led to interference of the drainage of the cerebral spinal fluid that bathes the brain, or he may have developed inflammation and fluid leakage within the substance of the brain.
Aides to Sharon said they were working on the assumption he would not return to work.
Sharon's deputy, Ehud Olmert, has
Doctors said it would take time to determine how much damage was caused by the widespread stroke Sharon suffered Wednesday night adding that media reports of permanent, significant damage were irresponsible.
Sharon's collapse less than three months before national elections also left his Kadima party, which he formed in November, in limbo.
In the short-term, Israelis appeared to still be supporting Kadima. A poll published in the Yediot Ahronot daily Friday found that an Olmert-headed Kadima would win 39 of 120 parliament seats, the most of any party and slightly less than the party polled under Sharon.
The dovish Labor Party would get 20 seats, and the hard-line Likud, which Sharon left to form Kadima, would capture 16 seats, according to the poll. The poll of 500 people was taken Thursday. It had an error margin of 4.4 percentage points. Some pollsters said the results might be influenced by sympathy for Sharon, and could change during the three-month campaign.
Peres would net 42 seats as head of Kadima, but some analysts said it was unlikely he would be chosen to lead the new party. He met with Olmert on Friday, but did not give details.
"We will know how to continue Israel's policy ... to continue Ariel Sharon's policies," Peres told reporters.
Whatever Sharon's political legacy turns out to be, there are many who believe he was the only man who could make peace between Palestinians and Israelis, and "the chances of that are fading as fast as Sharon's health," said Pizzey.
Palestinians reacted to the fall of their longtime enemy with a mix of glee and apprehension. Some Palestinian leaders worried that Sharon's illness could derail their Jan. 25 parliamentary elections. "We are watching with great worry at what might happen if he is harmed," said Palestinian leader Mahmoud Abbas, who called Olmert to express wishes for Sharon's recovery.
Some Palestinian children gave out sweets in the Gaza Strip at news of Sharon's illness.
Foreign leaders, who embraced Sharon following his unilateral pullout from the Gaza Strip last year, also expressed concern.
U.S. Secretary of State Condoleezza Rice praised Sharon as "a man of enormous courage," and British Foreign Secretary Jack Straw said he was praying for a miraculous recovery.
But Christian broadcaster Pat Robertson suggested thatfor "dividing God's land."
Sharon had been expected to win the March 28 election in a landslide as head of Kadima, which he formed after bolting Likud last year. Many hardline Likud lawmakers tried to torpedo the Gaza withdrawal and Sharon formed Kadima to free his hands to make further peace moves with the Palestinians.