"The government has lost control over the economy completely ... they are helpless. The stock market is in free fall and rupee is in free fall," said BJP leader Yashwant Sinha.
The former finance minister said the only thing that can stabilize the situation is for the government to resign and go for fresh elections.
The rupee slipped to 68.75 against the dollar on Wednesday.
"The prime minister is an economist and he has failed to control the Indian economy. He has no right to continue in his post if he is not able to control the economy," said BJP leader Shahnawaz Hussain.
Saying that the government has failed "miserably", BJP leader M. Venkaiah Naidu said: "It is a total mismanagement of economy and prime minister and finance minister must take the responsibility."
Finance Minister P. Chidambaram had on Tuesday said the rupee had overshot its true level and that the phenomenon of depreciating currency value is being faced by other emerging economies also.