Police detained two, including a local Jamaat-e-Islami activist, after the fire around 6:45am on Monday.
Another 12 other BNP-Jamaat activists were nabbed during raids in various parts of the city.
Boalia police OC Khandaker Nur Hossain said 25 to 30 masked men spilled petrol in the Awami League office next to the New Market in the suburbs around 6:45am.
Later they went away shouting anti-government slogans, said police quoting the locals.
The OC said they’ve had detained two suspects. One of them, Abdur Rashid Dewan, was a Jamaat activist.
Earlier miscreant vandalised a billboard of the Awami League in front of their Ward No- 30 office around 6am in Binodpur.
Meanwhile a hand-made bomb was exploded in front of the house of Ward No-30 Awami League General Secretary Shahidul Islam, said Motihaar Police OC Alamgir Hossain.