Unidentified assailants fired "indiscriminately" at worshippers at a Shia mosque at a northern Bangladesh town Thursday, leaving one dead and three others injured, police said.

Police said the attack happened at Shibganj, some 200 miles (125 kilometres) north of Dhaka, when Shia Muslims were holding their early evening prayers.

"So far one person has died after he was hit by bullets. The attackers entered the mosque and fired indiscriminately," local police chief M. Asaduzzaman told AFP.

Another police official Abdul Karim told AFP that "three other worshippers were injured after three or four unidentified assailants fired at 15-18 Shia Muslims as they were praying inside a mosque."

The gunmen fled after the attack and none was arrested, police said.

No one has claimed responsibility, but the assault came just a day after police shot dead a top Islamist militant accused of hurling grenades at the country's main Shia shrine last month.

The attack in Dhaka left two people dead.