The domestic unit had recovered to 68.65 in early trade on Friday as against Thursday's closing of 68.72.
The rupee on Friday bounced back by ten paise to end at 68.62 against the American currency on fag-end selling of dollars by banks and exporters on the back of recovery in the equity market.
The benchmark Sensex recovered 178 points to to close at 23,154.30 on fag-end buying ahead of the Union Budget after the Economic Survey projected the Indian economy to grow at 7-7.75 per cent in 2016-17, which could accelerate to 8 per cent in a couple of years.
Weakness of dollar in the global market also boosted the rupee value against the dollar, a forex dealer said.
The domestic unit resumed lower at 68.73 per dollar at the Interbank Foreign Exchange (Forex) market as against the Thursday's closing level of 68.72 and dropped further to 68.79 on initial month-end dollar demand from importers.
However, it recovered afterwards to end at 68.62 on fresh selling of dollars by banks and exporters on the back of recovery in the equity market, showing a gain of 10 paise or 0.15 per cent.
It moved in a range of 68.62 and 68.79 per dollar during the day. The dollar index was down by 0.02 per cent against a basket of six currencies in late afternoon trade.
The dollar was lower against the yen and the euro during Asia trade today, as jittery investors await a gathering of the world’s top finance officials over the weekend in China.
Market sentiment recovered as US stocks and oil prices gained overnight. Oil prices rose after Venezuela's oil minister said the country would meet with Russia, Saudi Arabia and Qatar on efforts to stabilize oil markets.
Pramit Brahmbhatt of Veracity Financial Services said, "Today the rupee opened near 68.73 on a negative note taking cues from 10-year bond yield as it rose to high point since February 3. We saw some sort of recovery since then on back of action from RBI as well as positive cues from domestic equity market.
"Where we saw Nifty rebounding from lower levels and gained nearly 60 points. Thus we saw the rupee appreciating by 10 paisa and closed at 68.62 mark."
Trading range for spot USD/INR pair is expected to be within 68.20–68.80 levels. In forward market, premium for dollar declined on fresh receivings from exporters.
The benchmark six-month premium July dropped to 194-196 paise from 196.5-198.5 paise yesterday and far-forward January 2017 contract also dropped to 413-415 paise from 416-418 paise.
The RBI fixed the reference rate for the dollar at 68.7775 and for the euro at 76.0404.
In cross-currency trades, the rupee inched up against the pound sterling to finish at 95.75 from 95.76 yesterday and also moved up against the euro to 75.59 as against 75.79 previously.
However, the domestic unit firmed up further against yen to finish at 60.78 per 100 yen from 61.22.