Bangladesh's elite anti-terrorism unit detained on Sunday three suspected members of a militant group believed to be behind a spate of recent attacks in the south Asian country.

Muslim-majority Bangladesh has seen a rise in Islamist violence in which liberal activists, members of minority Muslim sects and other religious groups have been targeted.

The detainees were members of the banned Jamaat-ul-Mujahideen Bangladesh and were arrested in a raid conducted in the northwestern district of Rajshahi, said Rumman Mahmud, a deputy director of the Rapid Action Battalion.

Sixteen crude bombs, seven petrol bombs and jihadi books were also found in their possession, he added.

The group is believed to be behind attacks such as the bombings of a Shi'ite shrine and the killing of two foreigners.

Islamic State has claimed responsibility for some of the attacks, including the killing of a Hindu priest last month, but the government has denied the militant group has a presence in Bangladesh.

At least five militants of Jamaat-ul-Mujahideen have been killed in shootouts since November, as security forces stepped up a crackdown on Islamist militants seeking to make the moderate Muslim nation of 160 million a sharia-based state.