This is Singh's first visit to Bangladesh after becoming Foreign Secretary in August.
Upon her arrival at the Shahjalal International Airport here, Singh was greeted by her Bangladeshi counterpart Shahidul Haque and Indian High Commissioner Pankaj Sharan.
Singh also called on Prime Minister Sheikh Hasina but details of the meeting were not immediately available.
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.
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Her visit comes two days before UN Assistant Secretary Oscar Fernandez-Taranco begins his Bangladesh tour amidst a standoff between the Awami League and the main Opposition Bangladesh Nationalist Party (BNP) over the polls.
Violence linked to political unrest since October has claimed over 50 lives. The BNP-led 18 party alliance has organised a series of blockades and strikes to push their demand for postponing the polls.
Violence escalated after the Election Commission announced the poll schedule last week and the opposition alliance called two back-to-back nationwide blockades.
According to sources in New Delhi, Singh will be reiterating Indian government's commitment to bring the Constitution Amendment Bill 2013 on LBA, a move which is facing stiff opposition from BJP and AGP, in the winter session of Parliament.
The LBA, an emotive domestic issue for Bangladesh, 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.