Two people were killed and another 25 were wounded in the latest attacks on Monday, when bombs ripped through court buildings in three Bangladesh towns.
The violence came after the August 17 countrywide explosions of more than 430 small bombs that killed two people and injured about 125.
"We are almost certain that Islamic militants carried out the attacks and they may repeat the violence," said a senior police official involved in the investigation. He spoke on condition of anonymity.
No group claimed responsibility for the attacks, but suspicion quickly fell on Islamic militants campaigning to establish strict Islamic rule in Bangladesh, a Muslim-majority nation governed by secular laws.
Leaflets from the banned Islamic militant group Jumatul Mujahideen Bangladesh were found at all blast sites after the August 17
Security officials discussed the possibility of more attacks at a high-level meeting late Tuesday, said another police official who was present at the gathering. He also spoke on condition of anonymity.
He said authorities have stepped up security ahead of the Hindu festival of the goddess Durga and the Islamic fasting month of Ramadan -- the two events feared to be the next target of attacks.
"The militants seem to create panic and draw public attention to their cause," the official said.
Hindus, who account for 10 percent of Bangladesh's 140 million people, celebrate the Durga Puja festival next week. Muslims are to begin the month of fasting on Thursday.