The Indian rupee was also supported by weakness in the dollar overseas after disappointing US jobs data announced last weekend eased concerns about the Federal Reserve's tapering of the stimulus programme, a forex dealer said.
At the interbank foreign exchange market, the Indian rupee opened strong at 61.52 a US dollar from Friday's close of 61.90. It moved in a range of 61.41 to 61.64 before settling at the opening level of 61.52, a rise of 38 paise or 0.61 per cent.
The Indian rupee is at the highest level since closing at 61.25 on December 11.
"It was a strong session for the Indian rupee, thanks to the weakness in the US dollar. Friday's poor non-farm payroll data led to losses in the US dollar...benchmark indices which closed on a strong positive note also helped Indian rupee to post gains," said Abhishek Goenka, CEO of India Forex Advisors.
The 30-share Sensex jumped 375.72 points, or 1.81 per cent, to notch up its biggest gain in seven weeks.
Overseas investors bought shares worth a net Rs 413.85 crore today and Rs 68.16 crore on Friday, according to provisional data with the stock exchanges.
"Indian rupee has started the week on a positive note, taking cues from the dollar index, which is trading weak for the third consecutive day as Friday's data showed the US economy had its weakest monthly job growth in three years in December," said Pramit Brahmbhatt, CEO of Alpari Financial Services (India).
"Local equities closed up by over 1.5 per cent ahead of CPI data, which is expected to be better than seen in November," he said.
Inflation as measured by the Consumer Price Index moderated to 9.87 per cent in December from 11.16 per cent in November, according to government data released after the markets closed.