At the Interbank Foreign Exchange (Forex) market, the domestic currency commenced slightly better at 53.00 a dollar from Monday's close of 53.01.
An initial rise in dollar demand pulled rupee down to day's low of 53.02, said dealers.
However, it later bounced back to a high of 52.78 as exporters were seen selling dollars on the back of fall in its value overseas and hopes of further decline in the wake of reports that Spain was considering requesting a line of credit from Europe's bailout fund.
The rupee finally closed at 52.87, a rise of 14 paise or 0.26 per cent over Monday.
Brokers said trading was very narrow with the rupee stuck in a 23-paise range.
Forex dealers said rupee also gained strength after RBI Deputy Governor H R Khan's comments that monetary and fiscal policy have to move in tandem.
"As we have articulated time and again, it (monetary policy) has to be in tandem with the fiscal policy. It has to be a joint venture. It is not a solo play," Khan said.
Meanwhile, the Indian stock market benchmark Sensex, which was up till afternoon, closed down by 135.85 points or 0.73 per cent on fag-end
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