Traders expect the local unit to continue trading with an upward bias, helped by record high local shares with the upcoming national elections being the key focus point.
Indian shares ended flat after hitting their second consecutive record high in as many sessions as blue chips such as Larsen & Toubro extended recent gains bolstered by buying from foreign institutional investors.
Foreign funds bought shares worth $240 million on Monday, taking their total purchases in 2014 to $2.6 billion. Foreign inflows into the debt market stand at a net $5.9 billion so far this year.
"The rupee is inching gradually higher to test the next resistance at 60.30 and major resistance at 60.00. As we approach the election dates, the market is betting on the formation of a stable government at the centre," said Param Sarma, director and chief executive officer at NSP Forex.
"We believe that the major resistance at 60 will hold as the central bank will be looking to buy the dollars to preserve export competitiveness in the background of global economic recovery taking shape," he added.
The partially convertible rupee closed at 60.48/49 per dollar compared with 60.77/78 on Monday. The unit rose as high as 60.43 during the session, its strongest since Aug. 1.
Dealers said losses in other Asian currencies and demand from oil refiners limited gains in the rupee.
Most emerging Asian currencies turned weaker as the Chinese yuan retreated, failing to keep earlier gains even though hopes for economic stimulus from Beijing could improve regional sentiment.
In the offshore non-deliverable forwards, the one-month contract was at 60.92 while the three-month was at 61.59.