Demonstrators chant during Almaz Atambayev’s speech and call on president to resign.
But he reluctantly accepted them after a week of protests and called the referendum after they were annulled in September by the country’s constitutional court for procedural violations.
The country’s 2.7 million registered voters began casting ballots at more than 2,200 polling stations at 6am (0000 GMT) on Sunday, with voting due to end at 8pm (1400 GMT).
Fifty per cent of the electorate has to vote for the referendum to be valid.
It is seen as a relatively democratic country surrounded by authoritarian governments in Central Asia.
Bakiyev has been involved in numerous standoffs with the parliament and is mindful that rigged parliamentary elections led to a revolution in 2005 that ousted his predecessor, analysts said.
Omurbek Tekebayev, an opposition leader, said: “Neither the parties nor the people will be able to prepare for new parliamentary elections that quickly. It would be unacceptable if they take place before the end of 2007.”
Bakiyev was elected by a landslide in an election in 2005 that was praised by Western election observers, but he has been accused by opposition leaders of high-handed tactics to hold on to power.