Higher shares also continued to underpin sentiment, with indexes gaining for a fifth consecutive session amid continued buying by foreign investors.
Overseas funds were net buyers for a third consecutive session on Friday with purchases of $97.56 million despite concerns about escalating tensions between Russia and the West.
"There is a strong foothold for the INR at 60 levels. There are no domestic triggers which can push the rupee sharply higher or lower from here. Market is now keen to see how the government delivers on its budget estimates," said Naveen Mathur, associate director, commodities and currencies at Angel Broking.
The partially convertible rupee closed at 60.30/31 per dollar compared with 60.28/29 on Friday. The unit moved in a tight range of 60.1650 to 60.32 range during the session.
Traders said gains in other Asian currencies versus the dollar also aided sentiment for the rupee.
Most Asian currencies rose on Monday, with the Thai baht touching a seven-month high, as investor risk aversion showed signs of easing, although market players remained cautious about geopolitical risks.
In the offshore non-deliverable forwards, the one-month contract was at 60.60 while the three-month was at 61.13.