The revised Bill, which takes into account the agreement reached between states and the Centre on contentious issues, will come up before the Cabinet, sources said.
The winter session concludes on December 23.
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In a compromise deal, the Centre on Monday had decided to keep petroleum out of GST and make some kind of constitutional mechanism for compensation to states for losses due to the new indirect tax system.
The launch of Goods and Services Tax (GST) has been hanging in balance for about four years now as states were concerned about their revenue losses on introduction of the new tax regime.