An elderly Hindu priest was hacked to death on Tuesday in Bangladesh, in what police suspect was the latest in a spate of attacks by Islamists on minority groups in the majority-Muslim country.

Three militants riding on a motorcycle killed Ananta Gopal Ganguly, 70, by slitting his throat when he was on his way to the temple he served in Jhenaidah district, about 100 miles west of Dhaka, police said.

"He left home this morning saying that he was going to a Hindu house to offer prayers," deputy police chief Gopinath Kanjilal told AFP.

"Later, farmers found his near-decapitated body in a rice field." 

The attack bore the hallmarks of previous killings by Islamist militants.

A 60-year-old Christian grocer was hacked to death on Sunday in an attack claimed by Islamic State.

The wife of a prominent anti-terror security official was also killed on Sunday, shot dead by three suspected militants on a motorbike.

As many as 40 people have been killed over the last three years by Islamist extremists, either members of religious minorities or secularist activists. While responsibility for the killings has been claimed by Islamic State and Al-Qaeda, the government has denied that either group is active in the country, blaming home-grown extremists instead.

The government has launched a crackdown on militant groups who want to impose strict Islamic law in Bangladesh.

Hindus make up about nine per cent of Bangladesh's 160 million population of mainly Sunni Muslims.

Additional reporting by Reuters.