"Paul Kagame has brought peace," said Eridigaride Niwemukobwa, 67, holding up her voter card proudly, while admitting she did not know for how long Kagame could to run Rwanda if the constitutional changes pass.
Polls opened in the capital Kigali on time at 7:00 am (0500 GMT), an AFP reporter said.
"There is no secret, I will vote yes," said Saidi Alfred, waiting in a line of around a hundred people to vote at a school in Kigali as polls opened. "It is because we want the president to continue to lead us."
By popular demand?
Some voters said they were not clear about the exact constitutional changes they were voting on, describing the ballot as a simple choice about whether to endorse Kagame or not.
"What interests me is that the president is reelected," Alfred said.
The proposed constitutional amendment would allow Kagame to run for an exceptional third seven-year term in 2017, after which he would also be eligible to run for two further five-year terms under the new rules.
Overseas voting among some 40,000 registered Rwandans took place on Thursday, but the main polls are taking place on Friday, when 6.4 million people are eligible to cast their ballots. Polls will close at 3:00 pm (1300 GMT).
Kagame has run Rwanda since his ethnic Tutsi rebel army, the Rwanda Patriotic Front (RPF), ended a 1994 genocide by extremists from the Hutu majority, in which an estimated 800,000 people were massacred, the vast majority of them Tutsis.
The issue of long-serving rulers clinging to power has caused turmoil in Africa, where some heads of state have been at the helm for decades.
Lawmakers in Rwanda, however, insist the proposed constitutional changes are the result of a popular movement, although Kigali has been criticised for stifling freedom of speech and the RPF has a pervasive presence at all levels of society.
Earlier this year, some 3.7 million people signed a petition calling for constitutional changes to allow Kagame to stand again.
In response to criticism, Kagame has said that "other nations" should not interfere with the country`s internal affairs, or his people`s wishes.
In an editorial on Friday, Kigali`s pro-government New Times newspaper said it expected the changes to pass.
"The referendum vote can only position him (Kagame) toward a path of choosing to continue stewardship of the country that has shaped from the ashes of the 1994 genocide against the Tutsi to the current glitter that it is," it said.
Open dissent `rare`
The proposed changes have been criticised by the United States and the European Union, as well as by the country`s tiny opposition Green Party.
The date for the referendum was only announced on December 8 with the Green Party saying it was impossible to organise a counter campaign to oppose the move at such short notice.
But Rwanda has made clear that criticism would not affect the outcome of the referendum.
"Citizens... make that important choice that will tell the world, that when it comes to defining the future of the country and the leadership to entrust with such a future, no one but Rwandans will have the last word," the New Times editorial added.
Provisional results are expected late on Friday, with final results to be announced before Monday, National Electoral Commission (NEC) executive secretary Charles Munyaneza has said, with over 600 domestic observers monitoring the polls.
Some Rwandans said they had boycotted the vote as the outcome was already known.
"We decided not to go to vote because we know the results already, so we should not waste our time," said a young Rwandan in Uganda on Thursday.
Carina Tertsakian from Human Rights Watch (HRW) noted that after "years of government intimidation... open expressions of dissent are rare," and that approval of the referendum was expected.
"As one man told us: It would be stupid to vote `no` because it won`t change anything," she added
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