Fears of Islamic extremism in Bangladesh are increasing following a knife attack on a church pastor.

Police told Associated Press that 52-year-old Luke Sarker, who leads Faith Bible Church in the north-western district of Pabna, was attacked by three men who came to his home saying they wanted to learn about Christianity on Monday.

Sarker said that the men tried to cut his throat, but he managed to raise the alarm and his wife came in, causing the attackers to flee. The pastor suffered only minor injuries.

Senior police official Siddikur Rahman told AP that investigators suspect the assailants were fundamentalist Muslims, though they have not yet been identified.

The incident follows the deaths of two foreigners last week. Italian aid worker Cesare Tavella was fatally shot on September 29, and Kunio Hoshi, a 65-year-old Japanese citizen, was gunned down four days later by masked men on a motorcycle. Islamic State have claimed responsibility for both shootings, and warned on Saturday that there would be more attacks.

"There will continue to be a series of ongoing security operations against nationals of crusader coalition countries, they will not have safety or a livelihood in Muslim lands," the group tweeted.

The Bangladeshi government has dismissed Islamic State's claims. "I can surely say that IS or any such type of organisation or their activities have not sprouted in Bangladesh yet," Prime Minister Sheikh Hasina told reporters on Sunday.

"Someone will post something online...why should we accept that unless we prove that? We cannot accept that."

Home Minister Asaduzzman Khan told AP that ISIS militants merely want to create "instability" in Bangladesh by claiming responsibility for the killings.

"Oh, it's absolutely rubbish, there is no IS in the country, no way," he said.

However, Bangladesh has had to deal with an increase in Islamist violence over the past year, including the killing of four atheist bloggers. More than 90 per cent of the country is Muslim, and despite a constitutional guarantee of free speech, atheism remains taboo.