“We are investigating whether it was a suicide attack or the attacker himself died in the blast when he tried to throw the bomb,” he said.
Bangladesh has suffered a wave of Islamist violence, with two foreigners, four writers and a publisher killed this year.
A series of bomb attacks on masques and Hindu temples has also rocked the country of 160 million people. Some of the attacks have been claimed by Islamic State.
The government has denied that Islamic State has a presence in the country. Police have blamed earlier attacks on home-grown Islamist militants.
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