"As a means of promoting ties between the two countries, this House and the other House would have the wisdom to endorse the land border agreement that I signed in Bangladesh," Singh said in Rajya Sabha while replying to Motion of Thanks to the President's Address.
Singh's appeal came at a time when BJP is opposed to the land swap agreement saying it would compromise country's territorial integrity.
Referring to the recent visit of President Pranab Mukherjee to Bangladesh, Singh said it was deeply appreciated by the people and government of that country.
He said this agreement would ensure peace and tranquility along the borders with Bangladesh and peace and order in both the countries.
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The Constitution Amendment Bill, cleared by the Cabinet last month, is likely to be tabled in the ongoing Budget session of Parliament.
The Bill, which will replace India-Bangladesh Land Boundary Agreement, 1974, involves exchange of 111 Indian enclaves in Bangladesh and 51 Bangladeshi enclaves on Indian soil.
Bangladesh has already ratified the pact. Indian enclaves in Bangladesh are spread over 17,149 acres, while Bangladesh enclaves in India are located in 7,110 acres of land.