The Syrian opposition and its Western allies have denounced the election as a sham designed to lend Assad a veneer of electoral legitimacy.
The government in Damascus, meanwhile, has touted the vote as the political solution to the three-year-long conflict that began as an uprising against Assad's rule.
Expatriate voting was to take place in Syrian embassies and consulates abroad where the staff has not defected to the opposition. Some European countries have said they will not allow Syrian expatriate voting to be held in their capitals. Polls would be open from 7 am to 7 pm but Syrian Ambassador in Beirut Ali Abdel-Karim Ali said voting could be extended further into the evening.
Many said they came to vote and show their support for Assad, including groups of men, women and children who carried Assad's photos and waved Syrian flags.
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"With our souls, with our blood, we will sacrifice for you, Bashar," they chanted.
There are about 1.1 million Syrians who live in Lebanon as refugees. Many among the refugees and opposition supporters abroad are expected to boycott the vote. The two other candidates in the race are mostly symbolic contenders and little known figures.
The conflict, now in its fourth year, has killed over 162,000 people and displaced one-third of Syria's prewar population of 23 million. It has destroyed entire cities and towns, left the economy in tatters and set alight sectarian hatreds in a society once known for its tolerance.