Some 27 million of Myanmar's 57 million people are eligible to vote, although it was unclear how many would vote on Saturday and how many will vote on May 24 instead.
But the cyclone has overshadowed the vote, which even before the disaster many saw as being skewed in the military's favour.
According to state-run Myanmar television, a week after the storm hit the death toll stands at 23,335, with 37,019 missing - both figures only slightly changed since Tuesday.
However Western diplomats in Yangon, Myanmar's former capital, say up to 100,000 people may have been killed by Cyclone Nargis, while more than one million have been left without shelter.
Many are without food and clean water.
State-run TV news repeated broadcasts urging people to vote, making no mention of the tens of thousands killed and missing in the cyclone.
"Those who value the national well-being should go and vote 'yes'," MRTV said in a scrolling headline.
The UN has called on Myanmar's government to focus instead on delivering aid to the 1.5 million cyclone victims who face disease and hunger and on Friday made a "flash appeal" for $187m to provide aid over a six month period.
Al Jazeera's Veronica Pedrosa, reporting from neighbouring Thailand, said the government was determined to push through the referendum which the ruling military hopes will secure backing for a new constitution.
"Despite the disaster - despite perhaps a million and a half people at risk of dehydration and starvation - this election is the absolute number one priority for the government," she said.
Al Jazeera correspondent Tony Cheng, who posed as a tourist to cross into northern Myanmar on Saturday, saw a heavy security presence on the streets as voting go under way.
He said there had been a lot of intimidation from the military for a yes vote to back the new constitution.
The new constitution is supposed to be followed in 2010 by a general election.
|The referendum has been delayed in areas |
hardest-hit by the cyclone [AFP]
Both votes are elements of what the military government has labelled a "road map to democracy" for Myanmar.
The draft constitution guarantees 25 per cent of parliamentary seats to the military and allows the president to hand over all power to the military in a state of emergency.
The rules would also bar Aung San Suu Kyi, the detained leader of the country's pro-democracy movement, from public office.
Her National League for Democracy party won a general election in 1990, but their victory was ignored by the military.
Anti-government groups and human rights groups, which have criticised the charter as designed to perpetuate military rule, have accused the government of neglecting cyclone victims to advance its own political agenda.
The Myanmar government has refused to allow foreign relief workers into the country to direct relief efforts, leaving humanitarian officials still waiting for visas a week after the cyclone struck.