More than 5 million Rwandans cast ballots Monday in the second presidential election since the 1994 Rwandan genocide campaign against the Tutsi ethnic community.
Kagame, expected to win by a landslide, was credited with bringing security to the country. He told reporters the election was a sign of progress for his country.
"When I have seen how they have expressed themselves, the people of Rwanda and all that has been done and said by the people of Rwanda, gives an impression to me that the process has been very democratic," the Rwanda News Agency quoted the incumbent as saying.
The incumbent leader was criticized for what his critics said was the elimination by assassination of many of his political rivals.
A journalist investigating the shooting of a South African general was killed in Rwanda at the order of the government, his editors said.
Meanwhile, in July, Andre Kagwa Rwisereka, a member of the opposition Democratic Green Party, was found dead in Rwanda with his head nearly cut off.
On Monday, Kagame faced fresh criticism that there was no viable or legitimate opposition movement vetting candidates in the presidential vote.
Kagame, however, said the international scrutiny was based on a Rwanda that existed more than a decade ago.
"Part of it is that this is Rwanda, an African country, so they have a certain mindset and views of what will happen here because (they think) Rwanda must be tribal, violent," he said.