The overwhelming favorite is Assad, who is expected to coast to victory. His current term expires in July.
Opposition representatives seeking to oust Assad have denounced the election as a sham designed to extend his rule. The government says no candidate will receive favored treatment.
Thursday was the deadline for prospective candidates to submit their names.
The balloting is slated for June 3 despite no sign of a respite in the ruinous war that has convulsed Syria for more than three years. In recent days, each side has been bombarding the other, causing huge numbers of civilian casualties in a conflict that has already killed more than 100,000 and forced millions from their homes.
Officials are expected to whittle down the final number of presidential candidates within five days. Each candidate must have the backing of at least 35 of the parliament's 250 lawmakers to make the final cut, among other requirements.
Assad succeeded his father, Hafez Assad after his death in 2000. The president is seeking his third seven-year term.
The elections will be the first presidential contest since constitutional reforms in 2012 mandated multi-party balloting and scrapped the previous referendum system.