The rupee pared its initial losses, but was still trading down by 3 paise at 68.08 per dollar in late morning deals amid sustained demand for the US currency from banks and importers.
The Indian unit resumed lower at 68.13 as against yesterday's closing level of 68.05 at the Interbank Foreign Exchange (forex) market.
The domestic unit hovered in a range of 68.11 and 68.19 during morning deals before quoting at 68.08 at 1113 hours.
The dollar index was up by 0.08 per cent at 99 against a basket of six currencies in early trade.
Globally, oil prices tumbled in Asia today after US commercial crude stock climbed to a record level, stoking worries about a global oversupply of the commodity.
The dollar weakened against the euro yesterday at the New York market after the release of an updated monetary policy statement from the Federal Reserve.
Meanwhile, the benchmark BSE Sensex was down 4.48 points, or 0.02 per cent, at 24,487.91 at 1115 hours.
The US dollar traded mostly steady against its major
rivals in early Asian trade, while pound sterling recovered from 31-year lows, bringing a reprieve for the currency after recent sharp declines in the wake of the UK's vote to leave the European Union last week.
Other major currencies were also steady, while China's central bank again allowed the yuan to weaken against the US dollar.
"Rupee opened stronger taking cues from weaker crude oil prices as well as negative dollar index. But at higher levels, rupee found some selling pressure that forced rupee to lower levels," Pramit Brahmbhatt of Veracity Financial Services said.
"Trading range for the spot USD/INR pair will be 68.20 to 67.50/USD," he added.
In forward market, premium for dollars inched up due to mild buying pressure from corporates.
The benchmark six-month premium for November moved up to 175-176 paise from 174-176 paise yesterday and far forward May 2017 contract also looked up to 368.75-369.50 paise from 367-369 paise.
Meanwhile, the benchmark BSE Sensex rose by 121.59 points or 0.46 per cent to close at 26,524.55.
