A stream of advisers, friends and government officials visited his hospital room on Sunday, praying he would wake up.
Acting Prime Minister Ehud Olmert, who took office after Sharon's stroke on 4 January, opened Sunday's Cabinet meeting with a birthday wish.
"Today is the birthday of Prime Minister Ariel Sharon. We all pray for his health and wish for his speedy recovery," Olmert said.
Sharon's sudden stroke shocked Israelis, suddenly incapacitating the country's most popular politician as he appeared to be cruising toward re-election.
But a smooth transition of power and the gravity of his illness have led most people to accept the reality of an Israeli government without the tough ex-general.
Raanan Gissin, a longtime Sharon adviser, said the prime minister is still on the minds of Israelis.
He said people constantly stop him on the street to ask when the prime minister will wake up.
Israelis are lacking "that feeling of stability that now is no longer in our daily life. We don't have it anymore and we're missing it very much," he said.
The mood at Jerusalem's Hadassah Hospital was sombre.
A stream of friends and officials
visited the Hadassah hospital
A few well-wishers bringing flowers to Sharon, who has undergone seven operations - including three brain surgeries - since the stroke.
"We don't celebrate. We come, we meet with other people who share the same experience and I'd say we just pray that he will wake up," Gissin said.
"Maybe this 78th birthday is a good opportunity to get up and see what's happening and take the necessary steps that we're all wishing for him to take," he added.
Israeli newspapers noted Sharon's birthday, quoting associates as saying it is a "very sad birthday."
Sharon has been unconscious since suffering the stroke.
He remains in critical but stable condition.
His doctors have said that with each passing day, his chances of recovery are slimmer.
Despite Sharon's absence, the centrist party he founded, Kadima, is expected to win a 28 March election with Olmert at the helm.