Ballots are still being counted, but early official results are at the half way stage point to a landslide victory, with Kagame taking 94.3% of votes counted so far, the electoral commission said on Tuesday.
The figure was based on results from 51 out of a total of 106 voting districts in Rwanda following Monday's election.
Electoral officials said four in five eligible voters had cast their ballots by midday, six hours after polling stations opened for the vote - which passed off peacefully with only isolated incidents reported.
The President has already thanked thousands of his supporters who assembled in Kigali's biggest football stadium to celebrate the result.
Other candidates for the presidency are not so satisfied with the way results are shaping up.
The main opposition hopeful, Faustin Twagiramungu, took just 3.5% of votes counted so far, with third candidate former minister Jean-Nepomuscene Nayinzira winning only 1.19%.
Ex-Rwandan Prime Minister
Faustine Twagiramungu not happy
Twagiramungu, a Hutu who returned from exile in Belgium to run in the election, has been accused of divisionism by government media as well as the electoral commission, a serious accusation in the traumatised country.
There were conflicting signals on Monday from the camp of Twagiramungu who, after voting, said he would abide by the results of the election as long as they were transparent.
"If they [the voters] choose somebody else, I will applaud that choice, as long as transparency prevails," he said.
‘No transparency’ claim
However his campaign manager, Ismail Mbonigaba, said: "Transparency has not prevailed. These results can only be questionable. One can only contest the results. We must not accept the results as transparent."
Mbonigaba ruled out any cooperation with the head of state: "How can we form part of a government headed by someone who has stolen our votes. We are not willing to form part of a government where people are taken hostage."
But neither the head of the electoral commission nor the head of the European Union observer mission reported any serious incidents that disrupted voting.
Kagame, 46, who heads the ruling Rwandan Patriotic Front (RPF) - the former Tutsi rebel movement which fought to end the genocide - had been widely expected to win the poll following a campaign marred by allegations of government-sponsored intimidation of opposition supporters.
He campaigned on a theme of national unity nearly a decade after up to a million minority Tutsis and their Hutu sympathizers were slaughtered in 100 days of vicious, government-orchestrated bloodletting.
"It's a big democratic step taken by our country," he said on Monday. "I am sure Rwandans like myself are happy that we've been able to make this huge stride."