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The rupee is higher around 61.82/83 versus Monday's close of 61.91/92 on the back of euro gains.
Local stocks are up 0.3%.
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% in 2013.
Dealers expect the pair to find support on month-end importer demand, but those would be good levels to sell.
The rupee is on course to end 2013 as Asia's third worst performer, down over 11%.
