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The rupee hit 13-month lows and bonds fell sharply as markets in the region tumbled on fears about the global economy.
It breached the 63 mark in early trade and is seen heading towards 64 this week as Foreign Institutional Investors (FIIs) are pulling out of Indian markets ahead of the year end.
At 11 am, the rupee was trading at 63.44 compared with previous close of 62.95 per dollar. It was last seen trading at these levels in 2013.
"Foreign investors are selling their investments in India and if it continues this way then the rupee may breach 64 this month itself," said a currency dealer with a private bank.
Currency dealers believe the central bank may step in later during the day to arrest the sharp depreciation. However, in a scenario where all emerging markets currencies are under pressure, intervention may be limited.
Russia sharply increased its benchmark interest rate on Monday, raising concerns about the global economy at a time of sliding oil prices and a weakening China economy.
"If the rupee weakness sustains for long, then we could see a delay in rate cuts," said Hari Chandramgethen, head of foreign exchange trading at South Indian Bank.
Traders said the rupee was also hit after data showed trade deficit widened to an 18-month high in November, in part due to surging gold imports.
Meanwhile concerns about foreign selling and delayed rate cuts sent the benchmark 10-year bond yield up as much as 10 basis points to 7.93%.
The yield had hit a 17-month low on Monday on hopes the RBI would cut interest rates after data last week showed consumer inflation slowing to the lowest on record.
Some analysts said they expected India to remain less vulnerable than other emerging markets.
"The strong central bank, improving domestic economy, political stability with a full mandate, falling inflation, low global crude oil and commodity prices, and a comfortable fiscal situation are major positives," said Samir Lodha, managing director at QuantArt Market Solutions.
There are also concerns on the street that the US Fed may decide to raise interest rates earlier than expected.
