There were seven or eight explosions at the Awami League headquarters, as leader Sheikh Hasina addressed a crowd, hurting about 200 people.
Prime Minister Khaleda Zia condemned what she called a “dastardly attack”.
No-one has yet claimed responsibility for the explosions.
Ms Hasina, who was slightly hurt, told the BBC she was protected by her supporters, some of whom were killed.
Ms Hasina accused the government of attempting to assassinate her and demanded it resign for failing to protect innocent people.
A government spokesman said the blasts appeared aimed at destabilising Prime Minister Zia’s administration.