At one stage, police obstructed them, triggering a clash.
BNP men attacked police with stones and clashes ensued, leaving 20 people wounded.
Police fired several rounds of tear gas shells to bring the situation under control, said superintendent of police Liton Kumar Saha.
After a seven-hour mass-hunger strike on Saturday, BNP announced hold rallies across the country, including in the capital, on Monday, demanding the immediate release of ‘critically’ ill Khaleda Zia for better treatment abroad.
Party secretary general Mirza Fakhrul Islam Alamgir announced the programme while concluding their hunger-strike programme in front of BNP’s Naya Paltan central office.
He said all units of their party in cities, district towns and upazila headquarters will hold rallies.