The two members of local hardline Islamist group 'Ansarulla Bangla Team' and three other militants were arrested after security agencies raided several areas here, police said.
The two were identified as 26-year-old Asif Adnan, the son of a former judge, and 24-year-old Fazle Elahi Tanzil, the son of a senior government officer, the Daily Star reported.
During questioning, Asif and Fazle admitted to planning to set up an al-Qaeda network in Bangladesh, a Dhaka police spokesman said.
The arrests come after al-Qaeda chief Ayman al-Zawahiri earlier this month announced the plans to launch a branch of the militant network to wage Jihad in South Asia, including India.
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Several militant groups operate in Bangladesh. But none of them have been linked to al-Qaeda so far.
The three other arrested militants were members of Harkatul Jihad (Huji) outfit.
The Detective Branch (DB) of the police also seized explosives, bomb making materials and electronic circuits from the possession of the three detainees.