Monday’s vote, which finished at 3pm (1300 GMT), went ahead peacefully and without incident, according to local authorities and observers from the European Union.
Incumbent President Paul Kagame of the Tutsi ethnic group, who heads the ruling Rwandan Patriotic Front (RPF), is widely tipped to win the poll, the first multi-party election in the tiny central African country since independence in 1962, and the first since the 1994 genocide in which up to one million Tutsis and moderate Hutus were slaughtered.
The main challenger to Kagame is former prime minister Faustin Twagiramungu, a moderate Hutu. A third, minor candidate, Jean-Nepomuscene Nayinzira, is also running.
The counting of the votes was due to start one hour after the closure of the polling stations. Early indications of results were expected Monday evening with provisional nationwide results due to be announced Tuesday by the National Electoral Commission .
Filled with hope
In the capital, Kigali, a school was turned into a polling station, nine years since it was the scene of one of the worst single massacres during the Rwanda genocide.
"Coming here to elect our president fills me with hope," said one young voter, waiting in a line of hundreds of people waiting to cast their ballots at the Kicukiro technical high school (ETO).
Polling monitor Hermogene Higaniro said that for those who survived the genocide, "coming here to vote is something like a symbol that allows them to turn the page."
"I am going to vote for the man who has brought us peace for these last nine years"
It was at this school that some 2500 people sought the protection of UN peacekeepers a few days into the 100 days of bloodletting that would claim up to a million lives between April and July 1994.
Scene of slaughter
A report by the human rights organization African Rights detailed what happened next:
"The Belgian (UN) contingent abruptly pulled out from the ETO on April 11 and the massacre of hundreds of civilians began even before the cloud of dust raised by the departure of the vehicles had time to settle."
Many of the refugees were murdered at the school, and most of the others were marched off and killed at a second site an hour away.
Juvenal Arawujo, 23, one of the few survivors of the massacre at the school, told the French news agency AFP, "The Belgian soldiers abandoned us. They did nothing to protect us."
Many of the 9000 voters registered at the polling station were clearly pro-Kagame but had abandoned their T-shirts and baseball caps bearing his image out of respect for the secret ballot.
Women put on their Sunday best, and many protected themselves from the sun with colorful parasols.
"I am going to vote for the man who has brought us peace for these last nine years," said Dassan Niyibizi.
Some four million Rwandans, or about half the population, were eligible to vote in the polls.