The Rwandan Patriotic Front (RPF), in power for 24 years, its allied parties and one critical opposition party are vying for 53 of the 80 seats in parliament.
The remaining 27 seats are reserved for women, youths and the disabled and they are elected by special councils and national committees.
“Our party is gaining momentum across the country despite numerous hurdles. We are hopeful that we will win at least ten seats in parliament,” said Frank Habineza of the Democratic Green Party, the only permitted critical opposition party, casting his vote in Kigali.
Habineza secured only 0.45 percent of the vote in last year’s presidential election. There were strict restrictions on opposition parties who were given only three weeks to campaign.
Currently all 53 seats up for grabs are held by the RPF and parties that are allied with it or back government policies.
Long queues of voters waited to cast their ballots. Polls opened at 0500 GMT and will close at 1500 GMT. Provisional results are expected late Monday.
“Turnout began as high as we expected and the elections are being conducted in a peaceful manner. In total we expect over six million voters and many youths who will be voting for the first time,” Charles Munyaneza, executive secretary of the National Electoral Commission, told AFP.
Instead of voting for individual lawmakers, Rwandans vote for a party that then decides the candidates to enter parliament.
To win at least one seat, a party has to get at least five percent of the total votes cast.
Kagame cast his vote from Rwanda’s embassy in Beijing on Sunday, where he is attending the Forum on China Africa-Cooperation (FOCAC).
Kagame has been the de-facto leader of Rwanda since 1994 when as a 36-year-old his rebel army routed extremist Hutu forces that slaughtered an estimated 800,000 people — mainly minority Tutsis — and seized Kigali.
His victory last year came after 98 percent of Rwandans approved a constitutional amendment in a 2015 referendum that granted him the right to run for a third term.
Kagame is hailed for his role in halting the genocide and turning around Rwanda’s economy but criticized for his iron-fisted rule, with rights groups regularly accusing him of ruling through fear and crushing free speech.
A prominent critic of Kagame, Diane Rwigara tried to contest the 2017 presidential election but was disqualified and arrested on charges of treason, inciting insurrection and forging documents.
Her mother is also in jail on similar charges and their family property was auctioned off on charges of tax evasion.