Three hours before the voting process officially ended, the Central Election Commission said more than 43 percent of the country's 2.3 million registered voters had already cast their ballots.
RFE/RL's Armenian Service reported that deserted polling stations in and outside the capital Yerevan seemed to contradict the election commission's claims.
Opposition leaders today openly questioned these turnout figures.
Koryun Arakelian, the deputy chairman of the opposition National Unity (Azgayin Miabanutyn) party, also accused President Robert Kocharian's government of fraud.
"The present referendum overshadows previous votes, during which we had documented many shortcomings. [Today] we noticed new forms of vote rigging, new ways of breaking the law that would certainly be useful in some other [countries]," Arakelian said.
To take effect, the proposed constitutional changes must be endorsed by at least one-third of Armenia's eligible voters and 50 percent of those who actually cast their ballot papers.
Regional political analysts had warned that even more than the opposition's calls for a boycott, the general apathy among Armenian voters would be the greatest challenge faced by Kocharian and his political allies.
The Armenian president was among the first voters who cast their ballots this morning.
Addressing reporters at a Yerevan polling station, he implicitly urged Armenian citizens to back changes that he described as democratic.
"Today, people in Armenia face this choice -- either to have more balance of power between the branches of government, or to keep a strong presidential system," Kocharian said.
To add weight to his remarks, Kocharian openly displayed his "Yes" ballot paper before television cameras.
Viktor Dallakian, a representative of the opposition Justice (Atarutyun) group in parliament, criticized the gesture as an infringement of the existing legislation.
"Kocharian has violated the Second Article of the Law on Referendums and Article Three of the constitution. These articles forbid open voting. By openly voting, the president is actually instructing others to vote 'Yes.' We regard this as a violation," Dallakian said.
In theory, the proposed changes are meant to transfer part of the president's prerogatives to the parliament, the government, and strengthen the judiciary. They should also allow millions of diaspora Armenians to obtain citizenship in the South Caucasus country.
The European Union, the Council of Europe's Venice Commission, and the United States have all backed the proposed changes, saying they are vital to the reform process in Armenia.
Rene van der Linden, the president of the Parliamentary Assembly of the Council of Europe (PACE), has described the referendum as "a chance for Armenians to show their commitment to Europe."
The PACE says the changes are in line with the commitments Armenia undertook when it joined the Council of Europe in 2001.
But opposition leaders argue that Kocharian has no right to modify the constitution. They claim that since he first came to power in 1998 he has consolidated his rule through rigged presidential and legislative polls.
The opposition had called upon voters to refrain from casting their ballots, saying the changes in reality aim at strengthening Kocharian's powers.
While urging voters to boycott the referendum, the opposition maintained its representatives in the country's Central Election Commission.
Justice (Atarutyun) representative Feliks Khachatrian today accused the authorities of intimidating regional election commission members on the eve of the vote.
"Yesterday [26 November], there was persecution and intimidation directed at commission members throughout the [country], up to the point that people broke into their homes at night and guarded their doors," Khachatrian said.
Government officials did not immediately react to Khachatrian's allegations, which could not be independently confirmed.
National Unity Party Chairman Artashes Geghamian said the irregularities that allegedly took place before and during the vote are worse than the fraud he said has taken place in previous polls.
"I feel sorry for the [ruling] coalition. I feel sorry for Mr. Kocharian. It is understandable that they started with gross [election] violations. But that they should end with such a level of violations will certainly affect Armenia's prestige," Geghamian said.
Yesterday, several hundred people demonstrated in central Yerevan to denounce the upcoming vote.
Defense Minister Serzh Sargsian -- whom many in Armenia see as a potential successor to Kocharian -- today ridiculed the opposition for failing to gather larger crowds against the referendum.
"If I organize any meeting and cannot have at least 1,000 people there in attendance, I would not commit suicide, of course. But I would definitely be very ashamed and unable to look into people's eyes," Sargsian said.
Opposition parties have threatened to call upon their supporters to take to the streets in case of fraud.
Kocharian had promised to ensure a free and fair vote and has also said he will respect any outcome.
Preliminary results are not expected until late today. International observers from the PACE and the Council of Europe's Congress of Local and Regional Authorities are due to give their assessment of the vote at a press conference on 28 November.
(RFE/RL's Armenian Service contributed to this report)