Earlier, the rupee resumed higher at 59.93 per dollar as against the last closing level of 60.01 at the Interbank Foreign Exchange market.
It gained further to trade at 59.85 per dollar in late morning deals amid bouts of dollar selling from banks and exporters.
It moved in a range of 59.80 and 59.99 per dollar during the morning deals.
In New York, the dollar continued to rise late yesterday as traders considered whether the solid US jobs report for June will put pressure on the Federal Reserve to hike interest rates sooner than expected.
Meanwhile, the benchmark 30-share index Sensex was trading lower by 42.85 points, or 0.16 per cent, to 26,057.23 at 1030 hours.