She said while the "porous" border has led to various illegal activities which need to be tackled effectively, the two countries should further explore cooperation in areas power, water, trade and connectivity.
Singh was speaking at the two-day conclave on India- Bangladesh Security organised by the Observer Research Foundation (ORF) and Bangladesh Enterprise Institute (BEI).
Her father T V Rajeswar, who was former Intelligence Bureau chief and later became a governor, was among the audience.
Listing steps to check illegal activities, she said officials at various levels including the director generals of Narcotics Control Bureau of both the countries are holding talks to address the issue.
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An MoU is also being signed between the countries to prevent infiltration, organised crime, human trafficking, illegal drug trafficking, circulation of fake currency notes (FICN), she said.
"If India is secure, Bangladesh is also secure. This issue goes to the core of what our common understanding should be," she said.
"We have seen from the experiences of another neighbour, our neighbour to the West that the forces of terrorism that are sheltered or encouraged will come back to destroy the very support structure that gave them sustenance in the first instance," she said.
The Foreign Secretary pointed out that both India and Bangladesh have come to a clear resolve that "we do not wish to harm each other. We wish to contribute to each others ecomonic progress, socio economic progress, development and stability".