Bangladesh has long become used to occasional explosions and killings but the latest attacks look increasingly like a concerted campaign of violence.
In leaflets left at some of the bomb sites a group called Jamatul Mujahideen Bangladesh admitted responsibility.
The militant organisation said its aim was to establish an Islamic state.
More than 90% of Bangladeshis are Muslims but their laws are mostly secular.
Jamatul Mujahideen also wants to get Britain and the United States out of Iraq
The group and another called Jagrata Muslim Janata Bangladesh were banned by the government earlier this year.
Finger pointing
Jagrata Muslim Jenata Bangladesh became notorious for a reign of fear in the remote town of Bagmara.
They held public executions of their opponents and suspended the corpses by their feet from trees.
Until now analysts have said they were not motivated by ideology but by local power struggles among criminals.
The government says it will find those responsible for the latest bombings.
But it has had little success solving earlier attacks.
In the past few years, cinemas, shrines and even the British High Commissioner have been targeted but there have been few arrests.
Making any investigation more difficult is a continuing acrimony between the opposition and the alliance government.
The main opposition party, the Awami League has claimed the government itself is behind some of the attacks, which the league says are intended to wipe out leading opposition figures.
The party points a finger at elements within Jamaat-e-Islami and Islami Oikka Jote, the two Islamic parties that are junior partners in the ruling coalition.
The government has strenuously denied the allegations and insists Bangladesh does not have a problem with Islamic militants.
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