The rupee was trading strong at 63.98 against the US currency on increased selling of the dollar by exporters and banks.
According to forex dealers, dollar's weakness against major world currencies overseas supported the rupee. Also, a strong domestic equity market propped up the rupee sentiment.
The domestic unit opened strong by 7 paise at 63.95 at the Interbank Foreign Exchange market today. It hovered in a range of 63.98 and 63.87 before quoting at 63.98, up 4 paise at 4.40 pm local time.
Yesterday, the rupee had declined by 11 paise to close at 64.02 against the US dollar amid renewed global tensions in the wake of North Korea firing a missile that passed over Japan.
Meanwhile, the 30-share BSE index Sensex ended higher by 258.07 points or 0.82 per cent at 31,646.46.
The dollar pulled away from the previous session's 4-1/2 month lows against the yen on Wednesday as investors' concerns over North Korea's latest missile test eased for now, while the Australian dollar surged on upbeat construction data.
The dollar index, which tracks the greenback's value against a basket of six major currencies, added 0.1 per cent to 92.292, having recovered from Tuesday's low of 91.621, its lowest level since January 2015. The dollar last traded at 109.77 yen, up from Tuesday's low of 108.265 yen, its lowest level since mid-April.