The rupee was trading strong at 64.37 in the evening session due to higher foreign funds inflows. The domestic currency also received a boost from fresh selling of the American unit by exporters and banks amid a firm domestic equity market.
Also, the dollar's losses against other currencies overseas supported the rupee sentiment.
The domestic unit opened strong by 10 paise at 64.35 at the Interbank Foreign Exchange market. It hovered in a range of 64.40 and 64.33 before quoting at 64.37, up 8 paise at 3.30 pm local time.
On Friday, the rupee had ended flat at 64.45 against the US currency in an otherwise quiet and range-bound trade amid weaker dollar sentiment overseas.
Meanwhile, the benchmark BSE Sensex ended the session higher by 54.03 points or 0.17 per cent at 32,074.78.
The US dollar nursed losses at a 10-month low against a basket of currencies on Monday as investors cheered upbeat Chinese data by piling into leveraged positions such as the Australian dollar and other high-yielding currencies.
Some of the biggest gains were seen in the yen crosses such as sterling, which was up 0.1 per cent on the day as investors added bets that US interest rates would rise very gradually in the coming months after the latest data.