During the meeting Hasina termed poverty as the common enemy of the region and underscored the need for working together to eradicate the menace, the prime minister's press secretary Abul Kalam Azad told reporters.
Singh later called on the main opposition Bangladesh Nationalist Party's chief and former prime minister Khaleda Zia.
Earlier, she held a meeting with Foreign Minister Abul Hassan Mahmood Ali. After the meeting with Ali, Singh told reporters that she had a very good discussion.
This is Singh's first visit to Bangladesh after becoming Foreign Secretary in August.
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Her visit comes in the backdrop of Indian government facing stiff opposition in Parliament to introduction of Indo-Bangla Land Boundary Agreement (LBA), an emotive domestic issue for Bangladesh.
The LBA envisages transfer of 111 enclaves with a total area of 17,160.63 acres to that country while there will be transfer of 51 enclaves with an area of 7,110.02 acres to India.
Singh's visit will be two days before UN Assistant Secretary Oscar Fernandez-Taranco begins his Bangladesh tour amid a standoff between the Awami League and the BNP over the polls.