Islamic State has claimed responsibility for murdering a Muslim preacher in Bangladesh, an online group that monitors extremist activity said on Tuesday, the latest killing declared by the militant group in the South Asian nation.

Islamist violence has surged in recent months in the Muslim-majority country, but the government has rejected Islamic State's claims, blaming the violence instead on homegrown militant groups.

The U.S.-based SITE Intelligence Group said Islamic State had claimed to have killed the man late on Monday in Jhenaidah, a district about 100 miles (161 km) west of Dhaka, the capital.

"Soldiers of the caliphate in Bangladesh were able to assassinate the polytheist apostate Hafidh Abdul Razzaq, one of the top preachers for the Rafidha religion," SITE quoted the group as saying.

Although the statement called the victim a member of the Rafidha religion, or the Shi'ite Muslim minority group, police identified the dead man as a homeopathic doctor, Abdul Razzaq, 45, and denied that he was a preacher or a Shi'ite.

Anowar Hossain, the officer in charge of the police station handling the case, said he was not aware the killing had been claimed by any militant group.

"We suspect local militants are behind the latest killing," he added. "The pattern of killing bore the hallmarks of previous killings of priests. He was not a Shi'ite. We have checked with his family."

Over the last few months, Islamic State has claimed responsibility for the killings of two foreigners, attacks on members of minority Muslim sects and other religious groups, but police say domestic militant group Jamaat-ul-Mujahideen is behind the attacks.

At least five militants of Jamaat-ul-Mujahideen have been killed in shootouts since November, as security forces have stepped up a crackdown on Islamist militants looking to establish a sharia-based Islamic state.