DHAKA, Bangladesh—A heavy crackdown on antigovernment protesters in Bangladesh has been fueling anger and fear within the country’s opposition movement, creating an opening for militant extremism to take root here, rights advocates and others say.

More than 100 people have died since January, when supporters of the main opposition Bangladesh Nationalist Party and its ally, the Jamaat-e-Islami, took to the streets to call for early elections. Police have arrested thousands of activists and banned the opposition groups from...