The rupee, which has been weakening in recent months, traded as low as 63.30 in midday trading.
The previous all-time closing low was 61.71 reached on Friday. On Monday, against the dollar, the rupee lost 2.4 percent.
The rupee has been hit among others by rising current account deficits, slowing economic growth, rising dollar demand from importers and a sharp outflow of funds from India in recent weeks. The likelihood of the U.S. Federal Reserve ending its easy money policies also has affected the rupee.
The rupee decline also caused yields on medium and long-term bonds to rise. The yield on the benchmark 10-year bond rose to nearly 9 percent.
Over the weekend, Indian Prime Minister Manmohan Singh, speaking to the Press Trust of India, sought to assure investors by saying the country is not headed toward a crisis and that there are enough foreign exchange reserves to finance up to seven months worth of imports.
In the stock markets, the 30-stock Sensex, which sank 769 points on Friday, extended its losses Monday, losing an additional 291 points, or 1.56 percent, to close at 18,598 points. The broader Nifty index, which lost 234 points on Friday, gave up another 93 points or 1.69 percent Monday to 5,415 points.
The Wall Street Journal said investors are growing increasingly worried about how India will fare in an era of tighter global monetary policy. They are also concerned about the government's ability to manage its economic problems as the rupee continues its decline.
The Journal quoted the latest research note by Nicholas Spiro, managing director of consulting firm Spiro Sovereign Strategy Ltd. in London, which said, "Sentiment towards India is souring not so much because of the country's weak fundamentals but because of the lack of credible policies to address them."