The rupee today gained 29 paise to close at the one-week high of 45.79/80 against US currency on renewed capital inflows and a weak dollar overseas.

Fresh dollar selling by exporters too boosted the rupee sentiment.

At the Interbank Foreign Exchange (Forex) market, which opened after two days holiday on August 31 and September 1, the domestic unit opened higher at 45.98/99 a dollar from last close of 46.08/09. Later it fell to the day's low of 46.00.

However, smart rally in local equities amid dollar selling by exporters helped the rupee to rebound to settle the day at 45.79/80, exhibiting a rise of 0.62%.

The benchmark Sensex today firmed up by 144.71 points or 0.87%, taking a total rise of 972.63 points or 6.13% in three-session of gaining streak.

Dollar selling by exporters near 46-level also aided the rupee rise.

Foreign Institutional Investors (FIIs) bought shares worth $253.18 million on August 29 and 30, after pulling out nearly $2 billion in straight ten trading days between August 12 and 26.

"Rupee ended up by over half% against the dollar, taking cues from global markets where dollar traded weak against the major currencies. Equities also closed higher by about 9.0% which further appreciated the rupee," Alpari Financial Services (India) CEO Pramit Brahmbhatt said.

"Now next support to look out for rupee is at 45.75 and the trading range for the USD/INR will be 45.75 to 46.10 tomorrow," he added.