Parrikar, the first Indian defence minister to visit Bangladesh in the last 45 years, held a meeting with Hasina's security adviser Major General (Retd) Tariq Ahmed.
No official statement was issued after the meeting but officials familiar with the talks said they discussed security cooperation between the two countries.
Parrikar, who arrived here today on a two-day visit leading an 11-member high-powered delegation, will meet the top civil and military leadership to strengthen defence ties between the two countries.
The vice chiefs of India's army, navy and air force, held talks with Bangladesh's three services' chiefs at their office in Dhaka cantonment, a defence ministry official said.
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"During the meetings, they discussed issues related to the existing good relations and cooperation between the armed forces of the two countries," an official statement said.
Top Defence Ministry officials in New Delhi had said the focus of Parrikar's trip was to deepen security ties and firm up a defence cooperation agreement that is likely to be signed when Hasina visits India next month.
Alongside India, Bangladesh has strong defence cooperation with China especially in military hardware.
Bangladesh Navy this month acquired its first submarines from China, as Dhaka sought to boost its naval power in the resource-rich Bay of Bengal.
Bangladesh Navy chief Admiral Muhammad Farid Habib during his recent visit to India had said Dhaka wants to work with the Indian Navy as there are many "non-traditional threats" in sea, a reference to piracy, floating armouries among others.