Mild dollar selling by banks and exporters in the face of subdued overseas sentiment alongside firm domestic equities largely supported the local currency, which struggled to stay positive throughout the day.
Forex market sentiment worldwide wobbled under renewed geopolitical risks amid concerns that North Korea may be preparing another missile test. The mood was also impacted by the rising political temperature in Europe.
There have been wide speculations about a US interest rate hike in December amid US Federal Reserve releasing minutes from its September meeting.
Meanwhile, domestic equities eked out gains to end in the positive zone as select buying in frontline FMCG, consumer durables, pharma and auto shares largely helped to offset some late-session selling pressure sparked by geopolitical worries.
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Most Asian bourses were closed today on account of holiday.
The Sensex rose over 32 points to close at 31,846.89, while Nifty gained 9 points to end at 9,988.75 after briefly scaling 10,000 mark.
FIIs and funds pumped in nearly Rs 5,000 crore into the country's debt markets in the last four trading sessions, primarily due to increase in the limit on foreign ownership of bonds.
However, in view of higher stock valuations, foreign portfolio investors (FPIs) pulled out more than Rs 550 crore from equities during this period.
At the Interbank Foreign Exchange (Forex) market, the rupee opened almost flat at 65.37 against the weekend close of 65.38 a dollar.
However, staging a strong rebound towards the fag-end trade, the rupee managed to end at 65.36, showing a gain of 2 paise, or 0.03 per cent.
The RBI, meanwhile, fixed the reference rate for the dollar at 65.3074 and for the euro at 76.5990.
The dollar index, which measures the greenback's value against a basket of six major currencies, was down at 93.52 after hitting a 11-month high last week.
In cross-currency trades, the rupee fell back against the pound sterling to finish at 86.11 from 85.57 per pound and dropped against the Japanese yen to settle at 58.02 per 100 yens from 57.87.
In forward market today, premium for dollar advanced further owing to sustained paying pressure from corporates.
The benchmark six-month premium payable in March inched up to 130.75-132.75 paise from 130-132 paise and the far forward September 2018 contract also moved up to 270-272 paise from 268.50-270 paise.
On the International energy front, crude prices gained some lost ground, after a 2 percent slide last week on growing expectations that Saudi Arabia would continue to restrain its output in order to support prices, and as the amount of rigs drilling for new oil in the United States dipped.
Brent crude futures, the international benchmark for oil prices, were up 16 cents, or 0.3 percent, at USD 55.78 a barrel.