It shot up further to 62.45 before quoting 62.50 per dollar at 1040 hours, hovering in a range of 62.45 and 62.70 per dollar.
Banks and exporters reduced their dollar positions on expectation of more foreign fund inflows into the equity market.
The benchmark Sensex rose 263.76 points, or 1.30%, to 20,481.15 at 1045 hours.
In the global market, crude oil futures traded sharply lower as markets reacted to a deal between Iran and major world powers that could head off further sanctions on Iranian crude.
WTI crude for January delivery fell 77 cents to $94.07 a barrel.