Reuters Market Eye - The rupee is higher around 61.82/83 versus Monday's close of 61.91/92 on the back of euro gains.
Local stocks up 0.3 percent.
The rupee is also helped by the foreign investment regulator's nod to Vodafone and Tesco's investment proposals, worth around $1.7 billion in total.
The dollar hovered within sight of a five-year high versus the yen on Tuesday and was on track for its biggest yearly percentage gain versus the Japanese currency in 34 years, having risen nearly 21 percent in 2013.
Dealers expect the pair to find support on month-end importer demand, but those would be good levels to sell.
The rupee on course to end 2013 as Asia's third worst performer, down over 11 percent.
Reporting by Subhadip Sircar