Paul Kagame, the incumbent Rwandan president, has secured a huge lead as balloting closed in the country's second presidential race since the 1994 genocide.
The election on Monday proceeded calmly although the run-up campaign was marred by arrests and killings, which critics said ensured Kagame faced no real competition.
The announcement of partial results for Rwandans living overseas, who voted on Sunday, flashed on a giant screen, giving Kagame 96.7 per cent of the vote.
The other three candidates got between 0.8 and 1.5 per cent.
The announcement of the final results is expected later on Tuesday.
Kagame won 95 per cent of the votes cast in the 2003 polls.
Chrysologue Karangwa, the chairman of Rwandan's electoral commission, said voting went smoothly across the country and that polling stations saw a high turnout.
Since the 1994 genocide when at least half a million people were slaughtered, Kagame has guided the country through a period of mostly peaceful prosperity, though the government cracks down harshly on dissent.
Tens of thousands of supporters started rejoicing at a giant rally in the Rwandan capital, Kigali, after the first results started coming in early on Tuesday.
Speaking to reporters after voting Kagame said the process was "very democratic" and dismissed allegations the real opposition was de facto excluded from the vote.
"The people of Rwanda were free to stand for election – those who wanted to – and to qualify, so I see no problem," he said.
"Some sections of the media seem to be reading from a different page."
'Facade for repression'
Kagame, 52, has been the de facto leader of this central African nation since his rebel group-turned-political party, the Tutsi-dominated Rwandan Patriotic Front (RPF), routed Hutu extremists after the genocide.
"What's important to remember is that none of the opposition parties have been able to present candidates, so voters don't actually have much of a choice"
Carina Tertsakian, researcher, Human Rights Watch
Despite being credited with ending the genocide, and ushering in stability and growth, critics say that Kagame's success is just a facade for a repressive regime.
Human Rights Watch said "a worrying pattern of intimidation, harassment and other abuses" has emerged over a period of six months.
"The past few months have been marked by an increasing crackdown on the opposition," Carina Tertsakian, a HRW researcher, told AFP from London.
"In this context it's not surprising people are afraid of speaking out and it's not surprising the polls are taking place in a relatively quiet atmosphere.
Added Tertsakian: "What's important to remember is that none of the opposition parties have been able to present candidates, so voters don't actually have much of a choice."