The election pits Kagame of the ruling Rwandan Patriotic Front (RPF) against Frank Habineza of the opposition Democratic Green Party of Rwanda and Philippe Mpayimana, an independent candidate, Anadolu Agency reported.
All three candidates ended their three weeks of electioneering in the capital Kigali on Saturday ahead of the polls.
More than 500 candidates are vying for 80 seats in the Chamber of Deputies, the lower chamber of parliament.
Polling stations opened at 7 a.m. local time (0500GMT) for more than 9 million eligible voters, according to the National Electoral Commission.
Around 100,000 voluntary polling officials were deployed to facilitate the free election at more than 2,500 voting stations. Polls will close at 3 p.m. (1300GMT) and ballot counting will begin after.
The electoral body accredited more than 1,100 local and international observers to monitor the elections.
They include those from the African Union, the East African Community (EAC) bloc, the European Union, the Commonwealth and the Economic Community of Central African States (ECCAS).
SD/PR