Union Ministers Rajnath Singh (Home), Arun Jaitley (Finance), M Venkaiah Naidu (Parliamentary Affairs) and V Sadananda Gowda held an hour-long meeting on the proposals of the two state governments but no decision has been taken.
The Ministers will meet again to carry forward the discussion process, official sources said.
While favouring the creation of Legislative Council, the two state governments reasoned that an Upper House will provide a better opportunity for people's participation in governance and decision-making.
Rajasthan government said the establishment of an Upper House would cost the state exchequer Rs 100 crore while Assam government said there would be a one-time cost of Rs 68 crore with a recurring annual expenditure of Rs 19 crore.
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A Parliamentary Standing Committee on the proposal of setting up of Legislative Councils in Assam and Rajasthan had recommended that the central government should evolve a national policy for the creation of an Upper House in state legislatures so that it is not abolished by the incumbent government.
Several social organisations also argued that members of various communities and ethnic groups which could not be sent to the Assembly could be accommodated in the council for fair representation.