The 36-hour shutdown called by the BNP-led 18-party alliance is being marked through clashes across the country on Tuesday.
Several vehicles were damaged at 9am at Adabar in the capital by Jubo Dal.
Jatiyatabadi Chhatra Dal brought out a procession in front of Mirpur Bangla College at 9am.
Prior to the procession, two cocktails were exploded at 8:45am. Later, another exploded during the procession, police said.
Another two cocktails were also went off at Adabar in Mohammadpur at 8:45am, police said.
Hartal supporters brought out a procession at Laxmibazar at 8:30am; police lobbed four rounds of tear gas.
Hartal supporters brought out a procession at Khilgaon at 8am in the capital Tuesday.
A laguna vehicle was vandalised, said AC Robiul Islam of Dhaka Metropolitan Police.
Two cocktails exploded at 7:50am in Badda area in the capital.
Meanwhile, two separate processions were brought out at Sabujbagh and Moghbazar by the hartal supporters.
Shibir brought out a hartal procession at Sanir Akhra at 7am, when a cocktail exploded, said OC Mizanur Rahman of Jatrabari thana.