The rupee opened higher at 63.76 per dollar at the Interbank Foreign Exchange as compared to 63.84 previously and firmed up further to 63.63 before ending at 63.64 per dollar, showing a gain of 20 paise.
The rupee had gained 32 paise or 0.50 per cent in the last five trading days.
The domestic unit moved in a range of 63.80 and 63.63 per dollar during the day.
In overseas markets, the euro today narrowed losses against the US dollar with investors keeping watch on developments in Greece.
Greece's bailout programme is expected to expire on Tuesday.
As well, the debt-burdened country was expected to miss a 1.6-billion-euro ($1.7 billion) debt repayment due to the IMF due the same day.