Motorcycle taxi driver Karangwa Vedaste said the voting process was calm and peaceful, but declined to say who he had chosen.
“I voted for a leader I trust. The one I voted for is a secret in my heart. We will share it when he wins,” Vedaste said.
The electoral commission barred eight other candidates, including Kagame’s most vocal critics, from running, citing a range of reasons including missing and incomplete registration documents.
Democratic Green Party candidate Habineza, whose deputy was found dead and almost beheaded in the run-up to the 2010 vote, said there had been signs of progress.
“We toured the entire country, and wherever we went, people welcomed us warmly. They gave us gifts and assured us they would vote for us,” Habineza said after voting.
“We have to maintain this momentum and not regress,” he added.
“We are confident, each of us is confident, it’s half and half,” independent presidential candidate Mpayimana told journalists after casting his vote.
The US State Department says on its website Rwanda has made “progress in developing national and local government institutions, economic development, maintaining security (and) promoting reconciliation.”
It also says it backs Rwanda efforts to “increase democratic participation (and) enhance respect for civil and political rights.”