President Pierre Nkurunziza's CNDD-FDD party won 64.03 per cent of the votes. The former rebel group National Liberation Forces (FNL) got 14.15 per cent, according to election commission chief Prosper Ntahorwamiye.
These results will only be definitive upon publication after a period allowing parties to legally challenge them.
On Friday, 12 opposition parties demanded the resignation of the national electoral board.
"Our position is crystal clear: we are still demanding the May 24 elections be invalidated and we also want the electoral commission to resign because it is not independent," said FNL leader Agathon Rwasa.
The United Nations' independent expert on the human rights situation in Burundi, Akich Okola, interviewed observers in Burundi to evaluate the elections. He said as far as he can see, the results reflect the will of the people. But he added that the necessary evidence might not be available to him.
"This is the third democratic elections that this country has held." said Okola. "I was priveleged to observe the second democratic elections in 2005 and this third series in this democratic process I think is indicating that Burundi is slowly maturing into a democratic state."