Police have detained BNP Standing Committee Member Gayeshwar Chandra Roy along with some other BNP men from Nayabazar area in the capital.
They were picked in a police car around 12pm after a clash.
Meanwhile, BNP has claimed that party's Dhaka Divisional Organizing Secretary Abdus Salam Azad has been arrested in connection with the clash during the program at the same spot.
BNP Standing Committee members Ruhul Kabir Rizvi, Gayeshwar Chandra Roy and other leaders and activists were present during the clash.
Gayeshwar Chandra Roy was injured in the clash.
The BNP at a rally on Friday announced that it was going to hold sit-ins at different entry points of Dhaka on Saturday to press home its demand for the general election to be held under a non-partisan government.