Buhari called for calm in northern Nigeria in an interview with the BBC, in his first public statement since the contested final election results were released on Monday.
They gave 57 per cent of the votes to incumbent Goodluck Jonathan, who was mainly supported in his native, Christian-majority south.
Since then, violence has intensified in the north.
Christian youths burnt a mosque in Kano early Tuesday. Muslims responded by destroying shops.
Earlier a prison was raided and its inmates set free.
The number of deaths has not been released for the moment. But an estimated 15,000 people have already been displaced since the beginning of the troubles at the weekend. Curfews are in place in various places in Kano city and Kaduna state.