The BAL won 106 contested seats, while ruling alliance partner Jatiya Party (Ersad) won 14 and the rest 20, according to unofficial results in 139 constituencies out of a total 147.
A re-election was required in eight constituencies where balloting had to be stopped because of violence.
24 people were killed in clashes between law enforcers and opposition activists during the voting on Sunday.
Meanwhile, 153 MPs were elected unopposed in polls where nearly 50 million voters failed to exercise their voting rights because of an opposition boycott.
Of the 153 seats, 127 candidates of Awami League and 20 of Jatiya Party (Ersad) and 6 others were elected.
Overall, Bangladesh Awami League won 233 seats - including 127 unopposed - out of the 300 directly-elected seats in the Bangladeshi Parliament.
Out of 40 registered political parties, only BAL and 7 alliance partners contested the election as main opposition Bangladesh Nationalist Party (BNP) and other parties - leftist, nationalist, centrist and Islamist - united on a boycott demanding that national election be held under a non-partisan caretaker government.
By Ferdous Ahmad
englishnews@aa.com.tr
