Mr Sharon has entered a 40th day in a coma but officials at Jerusalem's Hadassah hospital said his life was not in danger following the four-hour stomach surgery.
Doctors say the procedure was needed to repair damage to his digestive system which they believe was indicative of a wider systemic collapse.
The operation to extract around a third of Mr Sharon’s largest intestine came after doctors detected significant swelling to his abdomen.
Despite the success of the surgery, hospital director Shlomo Mor
Yosef emphasised that the abdominal problems were merely a further complication.
Dr Yosef said the 77 year old leader must still emerge from the coma that was medically induced after he suffered a massive brain
haemorrhage on January 4.
"It is important to re-emphasise that the general problem is his coma. It is not his abdominal pain," he said last night. "Every day
that passes, his chances of recovering are reduced."
But Ehud Olmert, who has taken over the reins of power, tried put a positive spin on the latest bulletin from the Hadassah hospital.
"We are encouraged by the reports from the hospital on the state
of the prime minister's health following his operation yesterday,"
he said at the start of the weekly cabinet meeting.
"The entire government embraces (Sharon's sons) Omri and Gilad
who are sitting at their father's bedside day and night."
While Mr Sharon is a revered figure, Israelis are becoming increasingly accustomed to the idea that the era of Sharon is
well and truly over.
Rather than sink in the absence of its leader, Sharon's newly-formed Kadima party has continued to operate without him over the past 40 days since his coma.
The latest batch of opinion polls have all forecast that Kadima should win around double the number of votes of its nearest rivals when Israel holds a general election on March 28.
Lior Horev, one of Sharon's senior advisors, said Kadima's strong lead in the polls showed that criticisms of the party’s success were wrong and that its wider political platform was a vote-winner.
"The prime minister's state of health is not of primary importance from the electorate's point of view," Mr Horev told Israeli radio.
In his first interview last week since taking over from Mr Sharon, Mr Olmert indicated that he planned to carry out more unilateral pullouts from the West Bank along the lines of Sharon's "disengagement" from the Gaza Strip last year.
He also pledged to strive to "redefine the borders of the state of Israel" in the coming years if elected - a project that Sharon was widely expected to have embarked on had he not collapsed 40 days ago.
Mr Olmert has also been handed the task of dealing with the fallout
of the radical Islamist movement Hamas's victory in last month's Palestinian election.
He reiterated in a cabinet meeting that he would have no dealings with a Hamas-led government which is expected to be formed after the new parliament holds its inaugural session on February 18.
A final session of the outgoing parliament should take place tomorrow.
"The moment the (outgoing) parliament breaks up, the rules of the game will change completely from Israel's perspective," Mr Olmert was quoted as saying in the cabinet.