Parrikar, the first Indian defence minister to visit Bangladesh in the last 45 years, met the President after holding talks with Prime Minister Sheikh Hasina's security adviser Major General (Retd) Tariq Ahmed to strengthen bilateral military and security cooperation.
The President told Parrikar that Bangladesh maintained "zero tolerance" policy in combating terrorism in "all its forms", a presidential palace spokesman told PTI.
The President urged the Indian minister to send more Indian military officials to Bangladesh for training to boost ties between the armed forces of the two countries, the spokesman said.
Hamid recalled with gratitude India's contribution to Bangladesh's 1971 Liberation War, saying "many valiant soldiers of Indian defence forces embraced martyrdom in the war," the spokesman said.
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Parrikar said terrorism is a global threat and India is working to establish peace in the region. He also sought joint efforts to enhance bilateral defence relations.
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.
"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.