The dollar index against its six major rivals was also almost stable.
The rupee commenced better at 60.40 a dollar from last close of 60.45 at the Interbank Foreign Exchange (Forex) market. It improved further to a high of 60.3550 on the back of surging domestic stocks to their new peak.
The Indian benchmark S&P BSE Sensex rallied for the sixth straight session and touched an all-time intra-day high of 26,674.38 before closing at 26,638.11 -also new closing high-, showing a rise of 77.96 points or 0.29 per cent.
Later, dollar demand from importers, mainly oil refiners, pulled it back to a low of 60.70 before recovering some ground to end at 60.50, a fall of five paise or 0.08 per cent.
The rupee gained 3 paise this week. This was its fourth straight weekly rise. For the month (August), rupee gained a marginal 5 paise.
Pramit Brahmbhatt, CEO, Veracity Group said,"Rupee traded weak as dollar demand from importers, mainly oil companies forced Rupee to end low. Local equities closed all time high which supported the rupee to some extent. The trading range for the spot rupee is expected to be within 60.20 to 60.80.
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