DHAKA: A series of blasts killed at least one person and wounded dozens as Shi'ite Muslims gathered for a procession in the old part of Bangladesh's capital early on Saturday to mark the holy day of Ashura, police said.

Islamic State - an ultra-hardline Sunni Muslim group that sees Shi'ites as apostates - claimed responsibility for the attack.

But Bangladesh's interior minister told Reuters that no militants were involved and the blasts were not linked to an attack that killed 16 people at a Shi'ite procession in neighbouring Pakistan hours earlier.

Police cordoned off the area and one officer said four suspects had been arrested.

Witnesses said people fled after blasts, losing their flip-flops and sandals in the panic.

Attacks on the Shi'ite minority have been rare in Sunni-majority Bangladesh, but Sunni militant groups have become more active.

"This is not a militant attack, rather it is a planned and destructive attack aiming only to destabilize the situation of the country," Interior Minister Asaduzzaman Khan told Reuters.

"Though the attack came hours after a suicide bombing in Pakistan, we strongly believe the situation is not similar at all as we live peacefully with Shia community," he said.

But soon after, monitoring group SITE reported Islamic State had released a message saying "soldiers of the Caliphate in Bangladesh" detonated explosive devices in Dhaka during "polytheist rituals".

At least 10 people were admitted to Dhaka Medical College Hospital, and most of them were in a stable condition, an official there said.

Mirza Fakhrul Alamgir, acting secretary general of the main opposition Bangladesh Nationalist Party, demanded a "neutral investigation" into the attack.

"This is a clear sign of a deteriorated law and order," said Moqbul Ahmed, the acting amir of the country's largest Sunni-Muslim Islamist party, Jamaat-e-Islami Bangladesh.

U.S. ambassador Marcia Stephens Bloom Bernicat released a statement saying she was shocked by the attack and noted Bangladesh's long tradition of religious tolerance and communal harmony.