The rupee depreciated by 5 paise to 64.06 against the US dollar in early trade on Thursday on month-end demand for the American currency from importers and banks.
Sustained foreign fund outflows and a strong dollar in global markets weighed on the rupee, currency traders said.
Domestic stock markets opening lower also weakened the sentiment locally, they said.
The US dollar advanced against the euro and yen after strong US growth data fuelled speculations that the Federal Reserve could consider hiking interest rate for a third time this year.
Yesterday, the rupee had ended on a flat note at 64.01 against the US dollar.
Meanwhile, the benchmark Sensex fell 50.58 points, or 0.15 per cent, to 31,595.88 in early trade today.