Twenty-four candidates submitted bids to run in the June 3 election that Assad is widely expected to win.
The court's spokesman, Majid Khadra, announced on Syrian state television Sunday that only three applicants met requirements of the election law to run.
Assad, who is seeking a third seven-year term, will face Hassan bin Abdullah al-Nouri, a 54-year-old lawmaker from Damascus, and 43-year-old Maher Abdul-Hafiz Hajjar, a lawmaker from the northern city of Aleppo.
The West has criticized the election as a farce as it comes during Syria's 3-year-old civil war.
Heavy fighting between rival Islamic rebel groups in eastern Syria killed 62 fighters and forced tens of thousands to flee their homes, activists said Sunday.
Meanwhile, talks continued over allowing rebels to leave the besieged Old City in Homs.
Rebels from the al-Qaeda breakaway group known as the Islamic State of Iraq and Greater Syria and fighters of the al-Qaeda-linked Nusra Front have fought each other for months over territory they previously captured together from President Bashar Assad's forces.
The rebel-on-rebel violence has raged in the north along the Turkish border that opposition fighters have controlled since a mid-2012 offensive. Earlier this year, it spread to Syria's east, home to most of the country's oil fields.
The Britain-based Syrian Observatory for Human Rights said the rebel infighting Sunday took place around three villages in the oil-rich Deir el-Zour province near the Iraqi border. In the past four days 62 rebels have been killed there, The Observatory said.
The rebel infighting has forced tens of thousands to flee the contested villages of Abreeha, Bseera and Sabha, The Observatory said. It gathers information through a network of activists on the ground.
Syria's conflict, which began with largely peaceful protests in March 2011, has evolved into a civil war with sectarian overtones that activists say has killed more than 150,000 people. Islamic extremists, including foreign fighters and Syrian rebels who have taken up hard-line al-Qaeda-style ideologies, have played an increasingly prominent role, dampening the West's support for the rebellion to overthrow Assad.
That has led to a backlash by Islamic brigades and more moderate rebels who launched a war against the al-Qaeda breakaway group the Islamic State of Iraq and Greater Syria. Fighting between opposing rebel groups has killed more than 3,000 people since the beginning of the year, activists say.
In Homs, a cease-fire held for a second day Sunday, but the planned evacuation of opposition fighters has not started, activists and a government official in the city said. The official told The Associated Press that talks were still taking place and "no new developments have taken place" in the city. He spoke on condition of anonymity because he was not authorized to reveal details of the ongoing talks.
Rebels in Homs, Syria's third-largest city, agreed Friday to surrender the territory in exchange for safe passage to other opposition-held areas. The agreement came after a blockade by Assad's forces caused widespread hunger in rebel-held parts of the city, which have been hit relentlessly by government artillery and airstrikes over the past year.
A local activist said the rebels expect to leave Homs as early as Monday.
"They are prepared to leave," the activist, who goes by the nickname Thaer Khalidiya, said. "They collected their personal belongings and weapons to protect themselves along the way in case of (cease-fire) breach."
Khalidiya said the rebels trust the government forces to stick to the deal, but fear that pro-government militiamen will attack them along the evacuation route.
Homs was once known as the capital of the Syrian revolution for its fierce opposition to Assad's rule.
Assad's forces have been taking back rebel-held areas throughout Syria in the past months with a mix of crippling blockades, deals with rebels and relentless pounding of opposition-held areas.