The rupee is trading at 54.28/29 versus its previous close of 54.02/03, tracking losses in the domestic equity market and a broad risk-off globally.
Stocks and commodities fell sharply in Asia on Monday as investors were rattled by a radical bailout plan for Cyprus and piled into safer assets including the U.S. dollar, gold and sovereign debt.
The Sensex is down 0.8 percent.
Most Asian currencies are trading weaker compared with the dollar.
Traders expect the pair to hold in a 54.10 to 54.40 range ahead of the RBI's policy review on Tuesday, where it is widely expected to cut rates by at least 25 basis points.
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