The National Election Commission said in 11 of 30 districts, Kagame won 93 percent of the vote in Monday's balloting, The New York Times reported.
Kagame, who has been in control of Rwanda since 1994, told supporters via his Web site the results are an "indication that Rwanda has respectable citizens."
Rwandans who supported Kagame told the Times they did so because the president has provided schools, roads, Internet service and a sense of peace and security.
Some Rwandans, however, complained about being forced to vote for him.
In the months before the election, several opposition leaders and journalists were jailed or killed.
Observers said none of Kagame's three challengers were considered a genuine alternative.
The leading opposition politicians who have spoken out against Kagame were barred from competing in the election.