Subdued greenback overseas along with abundant capital inflows into domestic equities largely supplemented strength to the local currency.
The upbeat trend was also supported by unwinding of long-dollar positions by speculators and local banks ahead of FOMC decision.
The US Fed will take centre-stage once again on the conclusion of its November FOMC meeting on Wednesday and subsequent release of its interest rate decision.
According to the latest depository data, FPIs invested a net sum of Rs 2,806 crore in the stock markets and another Rs 15,132 crore in debt, taking the total to Rs 17,938 crore (USD 2.75 billion) during October 3-27.
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In the meantime, the greenback gave back some of last week's strong gains in the midst of fresh US political risk.
Meanwhile, Brent crude hovered above the significant USD 60-barrel level supported by bullish near-term outlook.
At the Interbank Foreign Exchange (FOREX) market, the rupee opened slightly higher at 64.83 from Monday's close of 64.85 and largely traded in a tight range due to lack of fresh drivers.
After scaling a new intra-day high of 64.72 in late afternoon deals, the local unit finally settled down at 64.75, showing a rise of 10 paise, or 0.15 per cent.
The rupee has appreciated yesterday by a solid 20 paise.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 94.47 in early trade.
In cross-currency trades, the rupee declined further against the pound sterling to end at 85.55 from 85.46 per pound and also drifted against the Japanese yen to finish at 57.13 per 100 yens as compared to 57.07 earlier.
On the other hand, the local unit firmed up against the euro to conclude at 75.31 from 75.43 yesterday.
Elsewhere, the euro consolidates losses against the US dollar before the Eurozone inflation and GDP data, while sterling rose sharply ahead of Thursday's Bank of England policy meeting, which is widely expected to result in the first UK interest rate rise since 2007.
The benchmark six-month premium payable in March was steady at 115-117 paise, while the far forward September 2018 contract inched up to 257.75-259.75 paise from 257-259 paise previously.
On the International energy front, global crude prices traded stable in early Asian trade supported by ongoing OPEC led efforts to cut supplies, although the prospect of rising US shale output dragged.
Brent crude futures, the international benchmark for oil prices, were at USD 60.78 per barrel, down 12 cents.
US West Texas Intermediate (WTI) crude futures were at USD 54.05 a barrel, 10 cents below their last close.
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