At least 15 people have been killed in clashes between police and Islamic hardliners demanding that Bangladesh implement an anti-blasphemy law, police have said.

Eight people, including two policemen and a paramilitary soldier, were killed during clashes in Kanchpur just outside the capital, Dhaka, and another seven people died in Motijheel, a commercial area of Dhaka.

Protesters blocked roads in the area with burning tyres and logs during more than five hours of clashes, television footage showed.

The private United News of Bangladesh reported that violence erupted after security forces fired tear gas and rubber bullets in the central commercial district.

Islamic activists have been demanding that the government enact an anti-blasphemy law. The government in the Muslim-majority nation has rejected the groups' demands, saying Bangladesh is governed by secular liberal laws.

Dhaka metropolitan police said in a statement that all rallies and protests had been banned in the city until midnight on Monday for fear of further clashes.

Prime minister Sheikh Hasina's ruling Awami League and an alliance of 18 opposition parties led by former prime minister Khaleda Zia had planned rallies in Dhaka for later on Monday.

There was no immediate comment from the parties.