The BBC's Waliur Rahman in Dhaka says that the march went peacefully, although there had been a warning from the authorities that it could be the target of terrorist attack.
Thousands of police and members of the elite Rapid Action Battalion (RAB) guarded the route of the march.
The opposition alliance plans to organise similar marches in Dhaka and other cities and towns until Sunday.
The Bangladeshi Home Minister, Lutfozzaman Babor, said the police on Monday arrested no-one without valid reason.