Broad gains in the US dollar against emerging Asian currencies are also pressuring the Indian rupee, although trading is broadly seen range-bound ahead of December inflation data due next week.
Analysts widely expect easing vegetable prices will push down consumer and wholesale prices, allowing the central bank to keep interest rates on hold for a second consecutive month at its policy review on Jan. 28.
"It was a dull market. There were some (foreign fund) flows into the debt market which helped the Indian rupee hold up despite stocks being down," said Uday Bhatt, a foreign exchange dealer with UCO Bank.
"The factory output data on Friday and inflation next week will be key for future direction. Until then the 62.00 to 62.60 range on the rupee should hold," he added.
The partially convertible Indian rupee closed at 62.30/31 per US dollar compared to 62.31/32 on Monday. The rupee moved in a tight range of 62.30 to 62.47 during the session.
Indian shares fell for a fifth consecutive session on Tuesday, to mark their weakest start to a year since 2011, as software stocks including Infosys dropped on caution ahead of its October-December earnings results on Friday.
Foreign fund flows which have been a crucial support for the rupee will be closely monitored for direction.
Overseas investors turned buyers of Indian debt for the first time in six months in December, buying more than $850 million worth of bonds, and have purchased another $159 million so far in 2014.
Foreign funds are also net buyers of $119 million in stocks so far in 2014, after pumping in more than $20 billion last year.
In the offshore non-deliverable forwards, the one-month contract was at 62.68 while the three-month was at 63.55.
FACTORS TO WATCH
* US Dollar rebounds, gains limited by weak U.S. data
* Rupiah leads Asia FX losses, peso at over 3-yr low
* Europe shares edge up after Asia takes fresh hit
* Foreign institutional investor flows