Singh met Prime Minister Sheikh Hasina, opposition and chairperson of BNP Khaleda Zia and chairperson of the Jatiya Party General H M Ershad. She also met her counterpart Foreign Secretary M Shahidul Haque during her two-day visit.
During her meeting, Singh told Bangladeshi leaders that India wants successful completion of the election process.
"As a fellow democracy, India hopes that the forthcoming elections will strengthen democratic institutions, practises and processes in Bangladesh," she said.
"We hope that the forthcoming elections will respond to the aspirations of the people of Bangladesh and that they will be free, fair, impartial and peaceful and find wide acceptability," Singh said in a statement.
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Yesterday, she told reporters India will not "broker any deal or mediate" between Bangladesh's feuding political parties.
Singh's visit came in the backdrop of the Indian government facing stiff opposition in Parliament to the introduction of the 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 Bangladesh and the transfer of 51 enclaves with an area of 7,110.02 acres to India.
Singh told reporters that the two countries have made "concrete progress in our relations in the last few years".