Analysts are expecting a tight race that could go to a second round if no candidate wins more than 50 percent of the vote that was dominated by the threat of terrorist attacks.
Incumbent Burkina Faso President Roch Kabore was leading with just 12 of around 360 voting districts declared, the electoral commission said, a day after a presidential vote dominated by the threat of terrorist attacks.
Hundreds of thousands of citizens were unable to cast their ballots on Sunday because their polling stations remained closed for fear of attack.
Groups linked to Al Qaeda and Daesh operate across swathes of Burkina Faso, part of a widening terrorism threat in West Africa's Sahel, a semi-arid region south of the Sahara Desert.
An association of the opposition parties cast doubt on the credibility of the results on Monday, repeating allegations of irregularities and fraud during a joint news conference.
Ahead of the vote, international observers said they had seen no evidence of fraud.
More results on Tuesday
Kabore, who was first elected in 2015, led in most of the dozen voting districts whose results were announced on Monday afternoon, totalling over 53,000 votes, more than double as many as his nearest rival, Zephirin Diabre.
The electoral commission said further results would be announced on Tuesday.
Diabre is a former finance minister and 2015 runner-up. Kabore's other main competitor in the field of 13 candidates is Eddie Komboigo, the head of the party of Blaise Compaore, who was president for 27 years until a 2014 revolution.