Jamaat-e-Islami activists on Tuesday torched a Hindu temple in Chittagong and vandalized another in Lalmonirhat.
Bangladeshi Foreign Minister Dipu Moni condemned the Jamaat-e-Islami's attacks as "pure and simple terrorism." Alarmed by the rising sectarian violence, Bangladesh's government is considering banning the Jamaat-e-Islami organization.
Jamaat-e-Islami is the country's biggest Islamist political party.
"They want to create panic and weaken the law and order situation in the country by killing police," Bangladeshi police Inspector General A. K. M. Shahidul Haque told Niti Central news agency reported Tuesday.
Bangladesh, a largely Muslim country with roughly 160 million people, won its liberation from Pakistan in a 1971 war in which an estimated 3 million people died. Many Pakistani soldiers were abetted during the conflict by local collaborators.
While Jamaat-e-Islami opposed independence during the war, its leaders have subsequently denied committing atrocities against their countrymen during the struggle for independence.
Nevertheless, separatist Jamaat-e-Islami elements have continued their struggle against Dhaka's central authorities to establish a more Islamist friendly government in the country, which would incorporate Islamic Sharia legal principles as the basis for a reformation of Bangladeshi society.
Bangladesh's main opposition leader Khaleda Zia has condemned the recent attacks on Hindus by fundamentalist Jamaat-e-Islami militants and demanded their punishment.
"I called upon the administration and law enforcers to prevent such attacks on minorities with an iron fist," he said.
Heartening the tensions, last week top Jamaat-e-Islami leader Delawar Hossain Sayedee was sentenced to death for crimes against humanity during the 1971 war.
Since Saydee's sentencing, more than 60 people, including six police officers, have died in clashes between the Jamaat-e-Islami party's supporters and security officers.
A large number of Jamaat-e-Islami members played a crucial role in the 1971 Bangladesh war of independence and stand accused of atrocities committed during the conflict.
Following the conflict, Jamaat-e-Islami subsequently joined the Bangladesh Nationalist Party in an alliance and led a four-party coalition government during 2001-06, subsequently holding two ministries in Zia's government.
During Bangladesh's war of liberation Jamaat-e-Islami was an anti-liberation front that openly opposed the independence of Bangladesh from Pakistan, saying the country would have better prospered as an Islamic-dominated state under Pakistani rule.
Atrocity charges have dogged the Jamaat-e-Islami organization since independence. In 2010 Bangladesh's International Crimes Tribunal charged eight Jamaat-e-Islami leaders with crimes against humanity committed during the Bangladeshi liberation war.
Jamaat-e-Islami was also found guilty of forming paramilitary forces, such as Razakar and Al-Badr forces, and participating in genocidal activities against the population of Bangladesh.
On Feb. 28 Jamaat-e-Islami leader Delwar Hossain Sayeedi was convicted of genocide, rape and religious persecution during Bangladesh's 1971 liberation struggle and sentenced to death.