The dollar strengthened in the overseas markets which dampened the rupee sentiments, a dealer said.
At the Interbank Foreign Exchange (Forex) market, the domestic unit opened higher at 51.38/39 a dollar from overnight close of 51.47/48 and immediately touched a high of 51.35 on renewed selling of dollars by banks and exporters.
But, late it reacted downwards to close at 51.78/79 per dollar, showing a loss of 31 paise or 0.60 per cent on fresh dollar demand from importers amidst firm dollar overseas.
The BSE benchmark Sensex ended higher by 34.45 points or 0.20 per cent today.
In New York, the US dollar gained ground against most major currencies yesterday.
The rupee premium for the forward dollar settled higher on fresh paying pressure from banks and corporates.
The benchmark six-month forward dollar premium payable in September ended up at 155-157 paise from yesterday's close of 152-154 paise and far-forward contracts maturing in March also concluded higher at 286-288 paise from 278-280 paise.
The RBI fixed the reference rate for the US dollar at 51.5035 and for euro at 67.5415.
The rupee remained weak to close at 82.69/71 against the pound sterling from overnight level of 82.09/11 and moved down further against the euro to 67.68/70 from 67.63/65.
It, however, firmed up further against the Japanese yen to 63.65/67 per 100 yen from last close of 63.80/82.