DHAKA: Islamic State claimed responsibility for stabbing a Christian to death in Bangladesh as a "lesson to others", an online group that monitors extremist activity said, the latest killing declared by the militant group in the Muslim-majority nation.

The South Asian country has seen a surge in Islamist violence in which liberal activists, members of minority Muslim sects and other religious groups have been targeted.

The US-based SITE Intelligence Group said Islamic State claimed responsibility for killing Hussein Ali Sarkar in Kurigram, north of Dhaka.

The group reported on Twitter that a "security detachment" killed the "preacher" to be a "lesson to others".

Police said the 68-year-old victim converted to Christianity from Islam in 1999 but was not a preacher.

Kurigram district police chief Tobarak Ullah said three attackers stabbed him while he was having his morning walk on Tuesday.

"They left the scene exploding crude bombs to create panic," Ullah told Reuters by telephone.

"We have started an investigation into the murder. So far, we have not found any militant link."

Five men were picked up for questioning, he said.

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 the government has denied that the militant group has a presence in Bangladesh.

Police say home-grown militant group Jamaat-ul-Mujahideen, thought to have been lying low since six of its top leaders were hanged in 2007, was behind the recent attacks.

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

In 2005, the Jamaat-ul-Mujahideen set off nearly 500 bombs almost simultaneously on a single day, including in Dhaka. Subsequent suicide attacks on courts killed 25 people and injured hundreds.