In a communication to the General Secretary in charge of organisation Janardan Dwivedi earlier this month, the Commission said the process of holding organisational polls should be completed by June 30.
Since September, 2015, Congress has on two occasions urged the poll panel to allow it to defer its internal elections.
EC has said it would grant "no further extension" and the internal polls should be over "latest by June 30, 2017".
With the Commission refusing to grant further time to Congress to hold the organisational polls, the demand to anoint Rahul Gandhi party chief could gain momentum after the assembly elections are over on March 8.
According to rules, all registered political parties have to hold organisational elections annually. But Congress had cited its constitution to say that its internal polls are held every 5 years.
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