The suggestion was mooted by Prime Minister Narendra Modi to help save precious time and money spent in electioneering.
"BJP President Amit Shah has written to the Standing Committee on Law and Justice for holding simultaneous Lok Sabha and assembly elections," a senior BJP leader said.
Shah has also called for a larger debate among various political parties for holding polls to Lok Sabha and state assemblies concurrently and asked the Election Commission to explore such a possibility, the sources said.
The EC is not averse to holding simultaneous polls either and the matter is under consideration of a Group of Ministers headed by Home Minister Rajnath Singh.
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Making a strong pitch for it, Modi had said that due to frequent elections things get delayed and stalled and a lot of time is spent on elections. He also said a number of opposition leaders have met him and sought a way out.
The AIADMK has supported the idea in principle and so has the Asom Gana Parishad. The SAD said it supports the idea but has doubts on certain issues like mandate delivering a hung assembly.
Congress and Trinamool Congress have rejected the idea, saying "ideal as it may sound" is "impractical and unworkable". The NCP too said that the proposal is "not feasible". The CPI said the "proposal looks ideal" but there are practical problems such as need for mid-term polls.