Islamic State claimed responsibility for stabbing an elderly Hindu businessman to death in Bangladesh, monitoring service SITE said on Wednesday, in what would be the second killing by the militant group in the country in less than a week.

The Muslim-majority South Asian nation has witnessed a surge in Islamist violence in the past year in which members of religious minorities, liberal activists, academics and foreign aid workers have been killed.

Debesh Chandra Pramanik, 68, a shoe trader, was found hacked to death in his shop on Wednesday in the northwestern rural district of Gaibandha, police said.

Police found his body lying in pool of blood, police official Mozammel Haque said.

"The attackers slashed his throat with sharp weapons leaving him dead on the spot," he said, adding that one person had been picked up for questioning.

Islamic State claimed the killing of a village doctor on Friday.

The government has denied that Islamic State or al Qaeda groups have a presence in the country of 160 million and says home-grown Islamists are responsible for the wave of attacks.

State Minister for Foreign Affairs Shahriar Alam told Reuters in an interview published earlier on Wednesday that Islamic State was trying to ride a wave of religious radicalisation by falsely claiming killings, adding there was enough evidence implicating domestic militant groups.

Since February last year, at least 27 people, including five secular bloggers, a publisher and two gay right campaigners, have died in attacks linked to militant groups.

Islamic State has claimed 18 of the attacks since its first claim in September last year and Al Qaeda most of the rest, according to SITE.