Security forces across Bangladesh have conducted extensive raids after Wednesday's bomb blasts which killed two people and injured more than 100.
Security has been stepped up after the blasts
Officials say nearly 100 people have been detained or arrested so far in connection with the explosions.
The main opposition Awami League has called a general strike for Saturday, accusing the government of failing to act against crime.
More than 400 small devices went off simultaneously across the country.
An outlawed Islamic group, Jamatul Mujahideen Bangladesh, says it carried out the attacks.
Police in the south-western district of Satkhira say they have made progress in their investigation into the explosions.
The district's police chief Abdur Rahim said that two people have been arrested in connection with the blasts and they confessed to the police that they were involved in the attacks.
Rahim said the two men told police that they are members of a little-known Islamic group Ahle Hadith.
The leader of this group, Asadullah Al-Ghalib, was arrested in February this year and faces a number of criminal charges.
Meanwhile, officials in Bangladesh say the Prime Minister, Khaleda Zia, will cut short her visit to China.
Local government minister Abdul Mannan Bhuiyan said that the Prime Minister would return to Dhaka on Friday evening instead of Sunday as scheduled.
Security has been tight in all major towns and cities, with key installations such as foreign embassies, power stations, courts and government buildings under guard.
Reports say elite security forces using sniffer dogs searched for suspects and bombs in the capital Dhaka.
Ms Zia described the attackers as "enemies of democracy"
Bangladesh Prime Minister Khaleda Zia said the attackers were the enemies of democracy, while the United States called the bombings a heinous act.
US State Department spokesman Sean McCormack said the US "stands with the government and the people of Bangladesh as they work to hold to account those responsible".
Questions are also being raised about security in Bangladesh and the role of Islamic extremist groups in the country.
"Whoever did this made a big statement. It shows how fragile the security situation is here," a former army Brigadier General, Sakhawat Hossain, told AFP.
The Daily Star newspaper declared in an editorial that "each one of us in the country - government, opposition, or neutral - must today unite behind our common purpose to root out the terrorists and defend our democracy from this unprecedented assault".
In each incident, bombs were set off in crowded spots, mainly at government offices, journalists' clubs and courts, between 1030 and 1130 local time.
Officials said timing devices were found at the scenes of blasts but most of the bombs were small, homemade devices - wrapped in tape or paper.
Leaflets from the Jamatul Mujahideen Bangladesh were found at the site of some of the blasts.
"It is time to implement Islamic law in Bangladesh" and "Bush and Blair be warned and get out of Muslim countries", the leaflets said.
Early this year the Bangladesh government banned Jamatul Mujahideen and another group, Jagrata Muslim Janata Bangladesh
They were accused of being behind a series of bomb blasts, including those at two local aid agencies - Grameen and Brac.
The bans were seen as representing a major change in policy as the government had long insisted there was no threat from Islamic militancy.