At least 31 Syrian civilians and soldiers were killed in violence that continued Sunday while voters were casting ballots for a new constitution that the Syrian opposition and Western governments call a farce.

The constitution would create a multi-party system in Syria, which has been governed solely by the Baath Party since 1963. But even if it passes, President Bashar al-Assad still would be hugely powerful.

The opposition boycotted Sunday's vote. It says the only acceptable solution for Syria is Mr. Assad's ouster. His brutal military crackdown against a nearly year-long anti-government uprising has killed thousands of civilians. Syria calls the rebels foreign-backed terrorists.

U.S. Secretary of State Hillary Clinton Sunday said Syrian troops who still back Mr. Assad are dishonoring themselves. She said those who turn their backs on violence are heroes.

“And I want to reiterate my message to those Syrians who still support (Syrian President Bashar) Assad, especially members of the Syrian military and business community. The longer you support the regime's campaign of violence against your brothers and sisters, the more it will stain your honor. If you refuse, however, to prop up the regime or take part in attacks on your fellow citizens, your countrymen and women will hail you as heroes.”

But she also cautioned foreign governments against arming Syrian rebels. She said the terrorist groups al-Qaida and Hamas both support the rebels. Secretary Clinton said that unlike the situation in Libya, where she knew who was behind efforts to oust Moammar Gadhafi, it is unclear who is leading the Syrian fighters. She said no one knows where the guns and weapons would end up.

If approved, the constitutional referendum would drop an article making the ruling Baath party the leader of state and society. It would allow political pluralism and enact a presidential limit of two seven-year terms. But the limit would not be retroactive, meaning that Mr. Assad, already in power 11 years, could serve another two terms after his current one expires in 2014.

In areas like Homs, where government shelling has left hundreds dead, or in rebel strongholds in the northwest and south, voter turnout is likely to be low. Activists in Homs said no voting appeared to be taking place, and Internet video showed some people dropping ballots into the trash.

But in the capital, Damascus, where Mr. Assad retains support among religious minorities and the business class, many said they were eager to vote.

U.N.-appointed investigators estimate the death toll from the uprising at 6,400 civilians and 1,680 army defectors. Syrian government officials have said they only took military action when under armed attack from “terrorists.”