The 59-year-old is being challenged by Frank Habineza of the Democratic Green Party of Rwanda, and independent candidate Philippe Mpayimana.

Mr Kagame is credited with the country's rapid economic development since taking office in 2000.

But critics accuse him of suppressing dissent and political freedoms.

Polls across the country opened at 07:00 (05:00 GMT) and will close at 16:00.

Mr Kagame, who represents the ruling RPF party, has widespread vocal support, the BBC's Tomi Oladipo says.

The president has even referred to the vote as a mere formality, our correspondent adds.

He came to power in 1994, when his rebel group took control of the capital, Kigali, ending the genocide in which some 800,000 ethnic Tutsis and moderate Hutus were slaughtered.

Rwanda's constitution was amended in 2015, giving Mr Kagame a chance to stay in power until 2034.

The two challengers have complained that their supporters are being intimidated, which they say explains the low turnout at their pre-election rallies.

The candidates have also accused some local authorities of undermining their campaign.

The ruling party denies any accusations of wrongdoing.

Paul Kagame at a glance:

• Seen as military genius
• His rebel forces helped end 1994 genocide - he has been in power ever since
• Twice invaded much larger neighbour, DR Congo
• Accused of suppressing the opposition and ordering assassination of critics
• Sees Singapore and South Korea as models - economy growing at 7% a year
• Champions women's rights; most MPs are women