DHAKA (AFP) - The Islamic State in Iraq and Syria (ISIS) group claimed responsibility for the murder of a doctor who was hacked to death in western Bangladesh on Friday, according to a US-based monitoring group.

Police said homeopathic doctor Sanaur Rahman, 58, was riding a motorcycle in Kushtia town with his friend Saif uz Zaman on Friday morning when they were attacked by at least three men, who were also on a motorbike.

Rahman was killed while Zaman, a university professor, was seriously wounded.

"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.

While police had said earlier that the assault bore similarities to a spate of previous attacks by suspected Islamists, they also said a personal dispute could be the motive for the killing.

Zaman, a professor of Bengali literature at Kushtia's Islamic University, was critically wounded and flown by helicopter to Dhaka, 240km away, for emergency treatment.

"We are probing whether there are some other links including a connection to Islamist militants," police inspector Shahabuddin Chowdhury, who was at the scene, said.

Rahman's family said he was a popular doctor who handed out free medicine to the poor.

"He used to distribute homeopathic medicine to villagers at his garden house every Friday. We don't think he had any enemies," his brother-in-law Obaidur Rahman said.

The pair were both fans of a mystical musical tradition known as Baul, which is popular in Kushtia, with the doctor's brother-in-law saying Rahman used to arrange concerts at his home.

Bangladesh's "mystic minstrels" or Bauls have long been dismissed as hippies and even killed after being branded heretics by religious extremists in the Muslim-majority country.

Friday's attack comes amid a wave of murders of liberals, secular activists and religious minorities by suspected Islamist militants in Bangladesh.

A Buddhist monk was hacked to death last Saturday while an atheist student, two gay rights activists, a liberal professor, a Hindu tailor and a Sufi Muslim leader have also been murdered since last month.

ISIS and a Bangladeshi branch of Al-Qaeda have said that they carried out several of the killings.

But the secular government in Dhaka denies that the two extremist groups are behind the attacks, saying they have no known presence in the country, and blames the killings on home-grown militants.