The ISIS on Saturday claimed responsibility for the killing of a homoeopathic doctor in western Bangladesh, as the Muslim-majority country reels under a series of brutal murders of secular activists and minorities by Islamists.

"Fighters from the Islamic State assassinated a doctor who called to Christianity in Kushtia, western Bangladesh," the ISIS-affiliated Amaq news agency said in a brief Arabic message, according to SITE Intelligence Group.

58-year-old doctor Sanaur Rahman was riding home on his motorbike along with Saifuzzaman, assistant professor of Bangla literature at Islami University, when they were attacked by machete-wielding militants in Kushtia town on Friday.

Rahman was hacked to death while Zaman was critically wounded in the attack. He was flown to Dhaka for treatment.

A senior Home Ministry official rejected the claim "in the name of ISIS", saying "the home grown militants visibly are repeatedly trying to prove their links with international outfits like IS or al Qaeda".

"Our investigations found no link of any international group to the (recent) incidents in Bangladesh", additional home secretary Rahmatul Munim told PTI.

Kushtia police said both Rahman and his friend were fans of a mystical musical tradition known as Baul, which the Islamists consider as "un-Islamic".

According to residents in the neighbourhood, Rahman was a popular doctor as he used to treat and offer medicine to poor people free of cost running a free Friday clinic.

"We are investigating possible militant links to the attack but we also kept in mind if it was outcome of any personal enmity," a local police officer said.

Rahman was the latest victim of suspected Islamists who have killed several liberal and secular activists and religious minorities in Bangladesh in recent months.

A Buddhist monk was hacked to death last Saturday.

Earlier this month, a 65-year-old Muslim Sufi preacher was hacked to death by unidentified machete-wielding assailants in northwest Bangladesh, two weeks after a liberal university professor was killed in a similar attack claimed by the dreaded ISIS terror group.

The country's first gay magazine editor was brutally murdered along with a friend in his flat in Dhaka by Islamists two days after the professor's murder.

Less than two weeks ago, a Hindu tailor was hacked to death by machete-wielding ISIS militants in his shop in central Bangladesh.