The party is led by Tarique Rahman, who is expected to be elected Prime Minister when the final election results are announced.
Media estimates that the BNP has secured more than the 150 seats required for a majority in parliament.
The election is the first to be held since 2024, when student-led protests forced former Prime Minister Sheikh Hasina out after 15 years in power.
The Nationalist Party was banned during Hasina's time in office and has steadily increased in popularity since the uprisings.
