The domestic currency also snapped its two-day upmove when it had gained 21 paise against the US currency.
At the Interbank Foreign Exchange (Forex) market, the domestic unit resumed higher at 60.03 and improved further to almost two-week intra-day high of 59.98.
However, fag-end dollar demand from importers, mainly oil refiners, to meet their month-end requirements weighed on the rupee and it fell back to a low of 60.13 before settling at 60.12, a fall of three paise or 0.05 per cent.
The benchmark S&P BSE Sensex today gained 124.52 points, or 0.48 per cent, completing eight sessions of straight gains.
FIIs picked up shares worth Rs 652.40 crore yesterday, as per provisional data with stock exchanges.
The dollar index, a barometer of six major global rivals, was down 0.05 per cent.
Pramit Brahmbhatt, CEO, Veracity Group said: "Rupee continued to trade range bound and ended just below overnight close.Local equities continued its bull run and closed all time high which helped rupee to cap its fall. The trading range for the spot rupee is expected to be within 59.60 to 60.50."
Meanwhile, forward dollar premium ended stable to weak.
The benchmark six-month premium payable in December moved down to 217-219 paise from 219-221 paise previously while far-forward contracts maturing in June, 2015 finished stable at its overnight level of 462-464 paise.
The Reserve Bank of India fixed the reference rate for dollar at 60.0020 and for the euro at 80.6785.
The rupee edged up further against the pound to 102.31 from overnight close of 102.38 and also remained firm to 59.16 per 100 Japanese yen from 59.27.
It, however, fell back slightly to 81.00 per euro from 80.95.