The rupee hit a record low of 156.90 against the dollar during the session, weakening further from its previous all-time low of 156.50 hit on Wednesday.
The rupee closed at 156.85/95, weaker from Friday's close of 156.25/35.
"There was strong dollar demand today from both private banks and state banks for imports as companies which were closed for the traditional new year opened," a currency dealer said.
"Exporters are staying away and there are no inward remittances too."
The country's central bank governor Indrajit Coomaraswamy had said if the inflation rate could be maintained between 4 percent and 5 percent, the depreciation in the rupee would be around 2 percent or 3 percent.
The rupee has weakened 2.2 percent so far this year. It dropped 2.5 percent last year and 3.9 percent in 2016.
The central bank has bought around $400 million from the market in the first three months of this year to help build reserves and repay some debt.
Dealers said they expect the rupee to gradually weaken and face higher volatility this year due to debt repayments by the government.
Foreign investors sold government securities worth a net 1.8 billion rupees ($11.48 million) so far this year through April 18, the central bank data showed.