The rupee was trading strong at 66.67 in the mid-session on Tuesday on sustained selling of the American currency by exporters and banks.
Forex dealers said robust foreign fund inflows too supported the rupee.
The domestic unit opened strong by 4 paise at 66.67 at the Interbank Foreign Exchange market today.
It hovered in a range of 66.68 and 66.59 before quoting at 66.67, up 4 paise at 3.15 pm local time.
Yesterday, the rupee had gained 10 paise against the US dollar to end at 66.71 on fresh selling of the American currency by corporates and banks.
Meanwhile, the benchmark BSE Sensex was trading down by 50.4 points or 0.17 per cent at 28,997.79.
The dollar steadied on Tuesday as investors widely expect the Federal Reserve to raise interest rates next week and are waiting for clues on the likely pace of hikes, including this week's US job data.
The dollar index, which measures the greenback against a basket of six major peers, last traded at 101.65, ticking up from a one-week low of 101.22 on Monday.
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