Some 98% of voters support changing the constitution to allow him to run again in 2017 after his second term ends, the National Electoral Commission said.
Mr Kagame, 58, could remain in power until 2034 if the changes are passed.
The vote took place despite criticism of such an amendment by the US and other Western donors.
Rwanda’s electoral commission said 21 out of 30 districts had published results so far, covering about 70% of voters.
Full results are due to be released later on Saturday.
Mr Kagame has not said if he will run again, but he is widely expected to.
Asked at the polling station if he would stay on, he said: “What is happening is the people’s choice. Ask people why they want me.”
The arrogance of power
However, the US has said Mr Kagame should step down in 2017 to allow a new generation of leaders to emerge.
Rights groups accuse the government of stifling the media and political opposition.
The small opposition Democratic Green Party claimed it had been prevented from campaigning against the change.
Mr Kagame has been president since 2000 but has held power since 1994, when his rebel force entered the capital Kigali to end the country’s genocide.
Mr. Kagame has however been credited for transforming Kigali tremendously.
The debate over extending presidential terms has led to instability in other African countries such as Burundi and Congo Republic, but has not caused unrest in Rwanda.