The Syrian government said voters are flocking to polling centers across the country, the government-run SANA news agency reported.
Critics, however, say the draft constitution is a farce and are calling for the removal of President Bashar Assad as violence in Syria continued unabated, CNN reported.
Russia and China support the referendum process and accused participants in the Friends of Syria conference in Tunisia of fostering war, The New York Times said.
Assad and his wife, Asma, were greeted with cheering crowds of public employees when they arrived Sunday afternoon at a polling station in the state-run broadcast center in Damascus, the newspaper said.
Violence, however, kept voters from polls in areas such as Homs and Hama in central Syria.
At least 100 people were killed Saturday, opposition activists said. The anti-government Local Coordination Committees said 34 people were killed Sunday, mostly in Homs and Hama. The government also moved against protesters in several Damascus suburbs.
The Red Cross failed to reach a deal Saturday for a break in fighting so people trapped in the Baba Amr neighborhood of Homs could be evacuated. The BBC said the Red Cross is trying to reach two injured Western journalists and retrieve the bodies of two journalists killed last week.
The Red Cross has called for the government and rebels to stop fighting for two hours each day to deliver humanitarian aid to Homs and other cities.
Homs has been paralyzed by shelling and sniper fire for more than three weeks, opposition activists said.
The Syrian government said 13,000 polling stations were open Sunday for the country's 14.6 million eligible voters.
The government is touting the draft constitution as offering an end to the one party system that has dominated Syria for decades. Analysts, however, say the proposed constitution contains language that suggests government permission is needed to form a political party and won't change the fact that it's a minority-dominated situation, CNN said.
Ohio crash that killed two caught on camera [VIDEO]
Wisconsin business offering 'therapeutic cuddling' forced to close