"Sunil Gomes was hacked to death at his grocery store just near a church at Bonpara village," Shafiqul Islam, deputy police chief of Natore district where the murder took place, told AFP.
Another police officer, inspector Abdur Razzak, said the motive for the killing of 65-year-old Gomes was unclear.
But the attack was similar to those on Hindus, Buddhists and members of other religious minorities in Muslim-majority Bangladesh in recent months.
The murder came just hours after the wife of a top anti-terror police officer was stabbed and shot dead.
Three assailants riding a motorcycle shot Mahmuda Aktar, 33, when she was on her way home after putting her son onto a school bus in the port city of Chittagong, said Humayan Kabir, additional deputy police commissioner of Chittagong. They shot her in the head three times, Kabir told Reuters by telephone.
There might be a militant link as her husband Babul Aktar, superintendent of police, played an important role in apprehending top militants, Kabir said.
Bangladesh is reeling from a wave of gruesome murders of liberals, secular activists and religious minorities.
Police say more than 40 people have been killed by homegrown militants in the past three years, with a spike in attacks in recent weeks.
A Hindu trader was hacked to death last week, days after a homoeopathic doctor was also slaughtered along with a Buddhist monk.
International militant groups such as the militant Islamic State group and Al Qaeda's South Asia wing have claimed responsibility for most of the murders, but authorities deny these groups are present in the country.
Bangladesh's secular government instead blames political rivals. Experts say a government crackdown on opponents has pushed many towards extremism.The killing came just hours after the wife of a top anti-terror officer was brutally murdered in the southeastern city of Chittagong by suspected members of a banned local extremist group.
Bangladesh is reeling from a wave of murders of secular and liberal activists and religious minorities that have left more than 40 people dead in the last three years.
Authorities have blamed homegrown Islamists for the attacks, which have spiked in recent weeks, rejecting claims of responsibility from the Islamic State group and a South Asia branch of Al-Qaeda.
Bangladesh's secular government accuses political rivals of trying to destabilise the country. Experts say a government crackdown on opponents, including a ban on the largest Islamist party following a protracted political crisis, has pushed many towards extremism.
Another officer, Inspector Abdur Razzak, said the motive for the latest killing was unclear, but it was similar to those on Hindus and members of other religious minorities in recent months.
An Italian-born Catholic priest was shot and critically injured in the north last year -- an attack later claimed by Islamic State. Unknown attackers also tried to slit the throat of a pastor in another northwestern town.
- 'Innocent man' -
Father Bikash Hubert Rebeiro, from the Bonpara Catholic church, told AFP that Gomes, whose brother is also a priest, used to work as a gardener at the church and was "known for his humility".
"He attended Sunday prayers at my church and then went to his grocery store. The next thing we know he was hacked to death. I can't imagine how anyone can kill such an innocent man," Rebeiro said.
Hours before Gomes was killed, three unidentified men stabbed and then shot Mahmuda Begum in the head as she walked her son to a school bus stop near her home, said Chittagong deputy police commissioner Moktar Hossain.
Begum was the wife of Babul Akter who led several high-profile operations against the banned Jamayetul Mujahideen Bangladesh (JMB) militant group in Chittagong in recent months.
"We suspect JMB or local Islamist extremists for the attack. Akter led successful anti-militant raids in Chittagong in which several JMB men were arrested," Hossain said.
Home Minister Asaduzzaman Khan said the attack was revenge for Akter's role in tracking down militants.
"Babul Akter is a skilled and honest officer who played vital roles in combating militants. That's why they killed his wife as they could not find him," Khan told AFP.
A Hindu trader was hacked to death last week, days after a homoeopathic doctor was slaughtered along with a Buddhist monk. In all at least 10 people were killed by suspected Islamist militants in the last ten weeks.
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