Kabore, bidding for a second term at the helm of the troubled Sahel state, has 58.14 percent of the vote, according to the ongoing count conducted by the Independent National Electoral Commission (CENI).
The figures are derived from results from 196 out of the 368 districts, embassies or consulates where votes for Sunday’s elections were cast.
Kabore, 63, is seeking an overall majority from voting day to avoid a runoff in which he would stand against a single candidate backed by a united opposition.
He has been under fire for his response to a five-year-old jihadist campaign that has rolled in from Mali, claiming at least 1,200 lives and forcing around a million people to flee their homes.
Sunday’s elections were for Burkina’s legislature as well as its presidency, where executive power in the former French colony is concentrated.
Opposition parties say the vote was marked by fraud and flawed procedures. On Monday, they threatened to reject “results stained by irregularities.”
Their complaints include polling stations that either did not open or opened late, insecure handling of ballot boxes and arbitrary changes to voting areas.
Because of the unrest, the election was not held across at least one-fifth of the territory, denying up to 350,000 people of the right to vote, according to CENI’s figures.
Parties supporting Kabore on Tuesday argued that the problems encountered on Sunday affected “all the competing candidates and political parties” in a similar way.
The problems were not on a scale to have any major impact on the result, they said, urging all parties to respect the outcome.
An opposition protest was scheduled to take place early Wednesday outside the vote tabulation centre but was cancelled.
A joint observer team has been sent by the Economic Community of West African States (ECOWAS), the United Nations and the African Union (AU).
It has met with governing and opposition figures in what one of the mission’s members described as “preventative diplomacy.”