At the interbank forex market, the local unit opened at 73.87 against the US dollar, then inched higher to 73.84, reflecting a rise of 7 paise over its last close. The local unit also touched a low of 73.98 in initial deals.
On Wednesday, the rupee had settled at 73.91 against the American currency.
The Indian Rupee started on a flat note against the dollar on Thursday amid a decline in most Asian shares, Reliance Securities said in a research note.
The dollar index, which gauges the greenback's strength against a basket of six currencies, rose 0.01 per cent to 91.31.
''The US Dollar Index was flat this Thursday morning in Asian trade consolidating ahead of a key US jobs report that may provide clues on when the Federal Reserve will dial back monetary stimulus,'' the note said.
Global oil benchmark Brent crude futures rose 0.20 per cent to USD 69.10 per barrel.
On the domestic equity market front, BSE Sensex was trading 14.74 points or 0.03 per cent lower at 48,662.81 while the broader NSE Nifty rose 6.75 points or 0.05 per cent to 14,624.60.
Foreign institutional investors were net sellers in the capital market on Wednesday as they sold shares worth Rs 1,110.50 crore, as per exchange data.