When Chechnya's 430 polling stations closed at 6:00 p.m. local time, no noticeable incidents had been reported.
The elections took place amid high security out of fear that separatist forces would try to disrupt the voting process.
Media reports say thousands of army troops and police officers were deployed across the republic to prevent any incident.
Chechnya's Election Commission Secretary Ela Vakhitov said final official results will be released within two or three days.
High Turnout Reported
Election Commission Chairman Ismail Baykhanov in turn said over 60 percent of Chechnya's 600,000 registered voters took part in the vote. In the near absence of independent election monitors, Baykhanov's claim could not be verified.
According to the Chechen Constitution, at least 25 percent of voters should turn out for the elections to be technically valid.
Russia's RTR public television channel says the highest turnout was recorded in Tsentoroi, the fiefdom of late President Akhmad Kadyrov.
People in Tsentoroi sang and danced as Chechnya's Deputy Prime Minister Ramzan Kadyrov cast his ballot paper.
Kadyrov, who is the son of Akhmad Kadyrov, was appointed to run the government after Prime Minister Sergei Abramov earlier this month was injured in a car crash in Moscow.
Talking to reporters after voting, Kadyrov said he expected the polls to help bring peace to Chechnya.
"Our task is to end the war. It will end when there is no more shooting, killing or kidnapping here. And when all of the world's politicians who are not friends of our republic, and of Russia, leave us [alone]," Kadyrov said.
Chechnya's new parliament is designed to replace the current State Council that, in the absence of a proper legislature, has been serving as the republic's main legislative body.
State Council Chairman Taus Jabrailov, who recently withdrew from the election race amid speculations of growing disagreements with Kadyrov, told the "Kavkazskii Uzel" (Caucasian Knot) website on 27 November that the council would be disbanded as soon as both houses of the new parliament hold their first joint session.
Chechen President Alu Alkhanov today said the inaugural session would take place some time between 10 and 15 December.
According to the Chechen Constitution, the upper house of parliament, or Republic's Council, is made up of 18 members elected from single-mandate constituencies. The lower house, or People's Assembly, comprises 40 parliamentarians -- half elected from single-mandate constituencies, half from party lists.
Some 350 individual candidates and seven parties took part in Sunday's polls.
Candidates include a few Russian Army officers and scores of officials with the pro-Moscow regional administration.
Regional analysts expect candidates loyal to Kadyrov to win a majority of seats in both houses.
Talking to reporters after casting his ballot in his home region of Urus-Martan, Alkhanov said he hoped the new parliament would help bring economic stability to Chechnya.
"Today, the population expects the parliament to work actively with the government toward improving their living standards," Alkhanov said. "The parliament must ensure that the economy becomes more efficient and that laws are voted that will help market economy and investments develop with the greatest possible speed and efficiency."
Alkhanov also said that the high turnout testified to Chechnya's thirst for stability.
"There is a good turnout for these elections. The weather is great. The people [of Chechnya] are electing their parliament, the future members of their parliament. They're doing this with willingness and hope in the future," Alkhanov said.
Russia's ITAR-TASS news agency on 27 November reported that the overwhelmingmajority of the estimated 34,000 federal troops deployed in Chechnya had taken part in the polls.
Citing this and other circumstances, rights campaigners inside and outside Russia have described the vote as a simulacrum of a political process.
In a 60-page report issued this week, a coalition of Russian and western rights groups denounced the climate of fear that reigns in Chechnya.
The report -- co-authored by the International Helsinki Federation for Human Rights, the Norwegian Helsinki Committee, and Russia's Memorial rights group, among others -- criticizes the Kremlin's policy of progressively transferring its responsibilities to the pro-Moscow administration.
The groups argue that this policy has not brought peace to Chechnya. On the contrary, they say it has led to the further spread of fear and insecurity among the population.
The report, in particular, points at local private militias loyal to the Kadyrov family, which it describes as one of Chechnya's most destabilizing elements.
The Chechen separatist leadership has also denounced the elections as a political maneuver on the Kremlin's part.
Akhmad Zakayev, the exiled deputy prime minister of the separatist government, told RFE/RL's North Caucasus Service on 26 November the new parliament will have no legitimacy in the eyes of the resistance leadership.
"The position of our government has long been made public and is known to everyone. These elections do not have the slightest significance as a voting process that would express the people's will. [The Russian authorities] have found some puppet leaders and they're playing with them. 'Look at those Chechens,' they say, 'look at these people, they cannot live without Russia, they cannot live without close ties with Russia,'" Zakayev said. "This is a farce. These are not elections. This is not election day. This is a day that, in the name of the [Russian] people, has been designed to fool the entire world and the [Russian] people themselves."
Addressing an international forum at London's School of Oriental and African Studies on 25 November, Zakayev warned that the polls will lead to the further expansion of the theater of war and "push further away the day when there will be a real political solution in Chechnya."