Rwandans voted on Monday on a draft constitution that the government says would prevent a repeat of the 1994 genocide.
The government promises elections later this year
Turnout was reported to be high and voting peaceful.
The Tutsi-dominated transitional government says the new constitutional framework safeguards against the dominance of a single political party.
However, critics say it is geared toward keeping the Rwandan Patriotic Front in power and includes significant powers to curtail civil rights.
About 800,000 ethnic minority Tutsis and moderate Hutus died in the campaign of ethnic cleansing orchestrated by extremist Hutu authorities in 1994.
Correspondents say a majority of the country's nearly 4 million registered voters is expected to approve the country's fifth constitution since gaining independence from Belgium in 1962.
Prevents one party-dominance
Bans inciting ethnic hatred
Allows parliament to curtail free speech
At least half of registered voters must participate for the results to be validated. It has already been approved by parliament.
The ballot paper asked the question: "Do you accept the new constitution?" Voters put their thumb-prints in one of two boxes: "Yes" or "No",
Up for approval in this vote is a framework of a national assembly, senate, and president eligible to hold up to two seven-year terms in office.
Shops and offices were closed to allow people time to vote.
Aid agency vehicles have been requisitioned to transport ballots.
The draft constitution stipulates that no party can hold more than 50% of the seats in cabinet, even if they secure an absolute majority in parliamentary elections.
It also provides that the president, prime minister and president of the lower house cannot all belong to the same party and includes a new provision outlawing inciting ethnic hatred.
But one article in the proposed constitution in effect prohibits political campaigning at grassroots level, restricting it to provincial and national institutions.
Critics charge this is designed to strengthen the RPF's hold on power.
The draft also contains frequent reference to "national unity" as a priority.
Going against national unity was the reason given for the dissolution of the country's second-largest party, the Democratic Republican Movement, by the RPF-led parliament earlier this month.
The country is still deeply traumatised by the killing
Human rights groups, while noting the attention paid to rights within the draft, have also cautioned that it allows parliament to restrict those rights.
"The [draft] constitution confers on the government broad powers to curtail speech or meetings that are deemed divisive," said the New York-based Human Rights Watch.
If the new draft constitution is approved, parliamentary and presidential elections will follow later in the year, the government says.