Sharon said he did not think the stroke had affected his performance.
"I have to hurry back to work," Sharon told reporters as he left Jerusalem's Hadassah Hospital.
Sharon was rushed to the hospital on Sunday evening after showing signs of confused speech. Doctors said he suffered a mild stroke that left no damage, and he was unlikely to have another one.
Doctors say Sharon's stroke was the result of a small blood clot, which quickly broke up, after briefly blocking a blood vessel feeding his brain.
Sharon's aides say his condition improved considerably overnight and that he is in full control of the government, reports CBS News correspondent Robert Berger. He talked with his aides and doctors and was able to walk around the room and shower unattended.
Sharon's illness has sparked concerns by some about his ability to lead the country if elected to a third term in March elections.
"We're at the beginning of an election campaign. We're due to have general elections in Israel at the end of March. It does bring to the foreground the issue of his age and his health," said Jerusalem Post editor David Horowitz.
It also left his brand-new centrist Kadima Party scrambling. Without the 77-year-old Sharon, Kadima wouldn't likely amount to much, as the prime minister's popularity is the overriding factor behind the party's commanding lead in polls. With balloting three months away, concerns about his health could become a focus of the campaign, and improve the prospects of the hardline Likud Party that he quit to form Kadima.
Netanyahu, 56, a forceful public speaker who served as prime minister from 1996-1999, could be a formidable candidate, leading an attack on Sharon from the hawkish side, while the dovish Labor Party worries the other flank.
Though Likud dominated Israeli politics for nearly three decades, Sharon's exit has decimated its power base, with polls predicting a loss of two-thirds of Likud's seats in March 28 parliamentary elections, while Sharon's new centrist party, Kadima, enjoys a wide lead.
Netanyahu, who quit Sharon's Cabinet in protest just before Israel's summer pullout from Gaza and part of the West Bank, addressed happy backers early Tuesday and pledged to bring his party back to power.
Exit polls from all three Israeli TV stations showed Netanyahu receiving 47 percent of the vote in the Monday primary, while Foreign Minister Silvan Shalom got 32 percent, right-wing extremist Moshe Feiglin 15 percent and Agriculture Minister Yisrael Katz 6 percent.
Party officials did not wait for the official count to declare Netanyahu the winner.
Sharon underwent additional tests Monday after being rushed to Hadassah Hospital in Jerusalem on Sunday night, showing signs of confused speech. Israeli media reported he was unable to tell time or count fingers when he underwent preliminary neurological tests at the hospital, but doctors later said he improved quickly.
Sharon was treated with blood thinners and suffered no damage from the stroke, said his personal doctor, Boleslaw Goldman.
Hospital spokeswoman Yael Bossem-Levy said doctors ran more tests Monday and decided Sharon should also undergo brain and full body scans, procedures she described as routine.
Sharon held his daily staff meeting in the hospital, said aide Asaf Shariv. "He asked questions, he received an update from the military secretary and from the Cabinet secretary. He's in good spirits," Shariv told Army Radio.
Doctors recommended that Sharon, who is overweight, go on a diet.
Sharon has never released medical records, and a right-wing lawmaker and physician, Arieh Eldad, has demanded that the medical records be made public.
Sharon received calls from President Bush, Secretary of State Condoleezza Rice, British Prime Minister Tony Blair and Egyptian President Hosni Mubarak. Palestinian leader Mahmoud Abbas also sent wishes for a speedy recovery.
In Gaza Sunday, dozens of armed men from the Popular Resistance Committees, a small Palestinian militant group, fired guns in the air, screamed "Sharon is dead" and handed out pastries to motorists to celebrate the news that Sharon was ill.
Sharon led Israel's fight against the five-year Palestinian uprising, and many militants still see him as an enemy despite his pullout from Gaza earlier this year.
A leading member of Sharon's Kadima Party insisted that the prime minister's illness will not cripple the party.
"The prime minister's leadership is the cornerstone of Kadima, and will continue to be," Justice Minister Tzipi Livni told Army Radio. "But there is a worthy coterie as well," she said, referring to other ranking members of the party, such as herself and Finance Minister Ehud Olmert.
Sharon formed Kadima after concluding that his efforts to persuade Likud to support peace concessions were to no avail.