At the interbank foreign exchange, the rupee opened at 83.30 against the dollar and then touched a low of 83.32, registering a fall of just 2 paise over its previous close.
On Wednesday, the rupee settled at 83.30 against the dollar.
The rupee rose on Wednesday on flows from a Hong Kong-based bank amounting to USD 500 billion.
On Thursday, it opened at 83.31 as the US dollar index was at 102, while the US 10-year was stable at 3.93 per cent, said Anil Kumar Bhansali, Head of Treasury and Executive Director, Finrex Treasury Advisors LLP.
Bhansali further noted that Brent oil price rose to USD 78 per barrel as the Middle East supply worries and Houthi attacks continued in the Red Sea.
Brent crude futures, the global oil benchmark, rose 0.31 per cent to USD 78.49 per barrel.
Meanwhile, the dollar index, which gauges the greenback's strength against a basket of six currencies, was trading marginally lower at 102.42.
In the domestic equity market, the 30-share BSE Sensex was trading 374.43 points or 0.52 per cent higher at 71,731.03 points. The broader NSE Nifty advanced 97.50 points or 0.45 per cent to 21,614.85 points.
Foreign Institutional Investors (FIIs) were net sellers in the capital markets on Wednesday as they sold shares worth Rs 666.34 crore, according to exchange data.
On the domestic macroeconomic front, India's manufacturing sector growth fell to an 18-month low in December amid softer increase in factory orders and output, despite minimal inflation.
The HSBC India Manufacturing PMI survey, conducted by S&P Global, showed that there was a softer, albeit sharp, increase in factory orders and output, while business confidence towards the year-ahead outlook strengthened.