Opposition parties including the Left and the BJP say any inquiry on the issue must have a hard deadline. Some parties also want a parliamentary committee consisting of members from different parties to handle the investigation.
Parliamentary Affairs Minister Kamal Nath said the government is amenable to an investigation. "The issue of Wal-Mart lobbying is not a concern only for opposition but also for the Government of India," he said in Parliament.
The new controversy is fomented by a disclosure in the US that Wal-Mart spent Rs 125 crores in the last four years on lobbying for access to different markets including India.
The US said today that Wal-Mart has not violated any law. The American ambassador to India, Nancy Powell, told NDTV that her country makes a very clear distinction between bribery and lobbying.
In November, Wal-Mart informed the US Securities and Exchange Commission that it was investigating potential violations of the US Foreign Corrupt Practices Act in Brazil, China and India, among other markets. The company's joint venture in India - Bharti Wal-mart -suspended several employees as part of an internal corruption investigation.
Authorities are also investigating Wal-Mart for possible violations of foreign investment rules in India, relating to a $100 million investment in a company owned by its wholesale joint-venture partner, Bharti Enterprises, which has said that no laws were broken.
Last week, the government won a vote in Parliament on its decision to allow Foreign Direct Investment or FDI in retail. The vote was non-binding but tested the ability of the minority government to help push important legislation and reforms.
The government was reduced to a minority in September when the PM decided to introduce new economic reforms led by FDI in retail. Mamata Banerjee's Trinamool Congress exited the coalition in protest
The reforms, economic experts and investors believe, will shore up a slowing economy and bring in a fresh infusion of investment, which could also help farmers and small businesses.
However, opposition parties say the new policy will crush small retailers not able to withstand the competition from global giants.
(With inputs from Agencies)