Russian officials say more than 50 percent of eligible voters went to the polls for a referendum in Chechnya, making the vote valid under Russian law.
Electoral officials say that by late in the day, more than 50 percent of the nearly half-million eligible voters had cast their ballots, the level needed for the referendum to be declared valid.
The voters are being asked to approve a new constitution for Chechnya.
Voters from Chechnya, refugees in neighboring Ingushetia and Russian soldiers based permanently in Chechnya took part in the poll. Aside from the constitution, participants were also asked to approve a series of laws related to eventual presidential and parliamentary elections in Chechnya.
Despite rebel threats of violence, the vote went off amid relative calm for the restive republic.
Russian President Vladimir Putin has portrayed the referendum as a path to peace and offered to grant Chechens a broad degree of autonomy within the Russian Federation.
But Chechen separatist leader Aslan Maskhadov has rejected that offer, saying the rebels will settle for nothing less than full independence.
Mr. Makhadov also favors peace talks with the Kremlin. But presidential aide Sergei Yastrzhembsky has again ruled out such talks.
President Putin scheduled the referendum amid increased pressure to negotiate a political settlement, after armed Chechen rebels stormed a Moscow theatre last October, taking hundreds of people hostage.
Chechnya has operated under de facto independence since Russian forces abandoned their first Chechen campaign in 1996. The Russian army returned in 1999 after a series of apartment building bombings in Moscow and elsewhere that the Kremlin blamed on Chechen separatist rebels.