Robertson's comments drew widespread condemnation from other Christian leaders, President Bush and Israeli officials, who canceled plans to include the American evangelist in the construction of a Christian tourist center in northern Israel.
In a letter dated Wednesday and marked for hand delivery to Sharon's son Omri, Robertson called the Israeli prime minister a "kind, gracious and gentle man" who was "carrying an almost insurmountable burden of making decisions for his nation."
"My concern for the future safety of your nation led me to make remarks which I can now view in retrospect as inappropriate and insensitive in light of a national grief experienced because of your father's illness," the letter said.
"I ask your forgiveness and the forgiveness of the people of Israel," Robertson wrote.
The 77-year-old prime minister suffered a devastating stroke Jan. 4 and remained hospitalized Thursday in critical but stable condition.
A scan of Prime Minister Ariel Sharon's brain
Thursday's brain scan showed that the remnants of blood from Sharon's massive cerebral hemorrhage last week had been absorbed, hospital officials said. As a result, doctors removed a tube they inserted into Sharon's skull to relieve pressure on his brain, the statement from Hadassah Hospital said.
Doctors also attached a new intravenous line into Sharon's arm to prevent infection.
Medical experts, meanwhile, raised new questions about whether blood thinners that Sharon received after a Dec. 18 stroke contributed to last week's massive brain hemorrhage.
Ending the sedation, which has kept Sharon in an induced coma for the past week, is a key step toward assessing the damage from the stroke. Hospital spokesman Ron Krumer said it was unclear when the sedation would be halted.
The day after Sharon's stroke, Robertson suggested he was being punished for pulling Israel out of the Gaza Strip last summer. The pullout was seen by many evangelical groups as a retreat from biblical prophecy of Jewish sovereignty over the area.
"God considers this land to be his," on his TV program "The 700 Club." "You read the Bible and he says 'This is my land,' and for any prime minister of Israel who decides he is going to carve it up and give it away, God says, 'No, this is mine."'
Despite the apology, it was doubtful Robertson would be brought back into the fold of the proposed Christian Heritage Center in the northern Galilee region, where tradition says Jesus lived and taught.
The exclusion carries a special irony for a preacher who helped define television ministries: The planned complex is to include studios and satellite links for live broadcasts from the Holy Land.