The rupee resumed higher at 54.30 per dollar as against the last weekend's level of 54.47 at the Interbank Foreign Exchange (Forex) Market and moved up further to 54.26 against the American currency.
However, it declined afterwards to 54.45 before quoting 54.37 per dollar at 1040 hours.
It hovered in a range of 54.26 and 54.45 per dollar during the morning deals.
Sustained capital inflows from foreign funds into equity market mainly boosted the rupee value against the dollar, a forex dealer said.
Foreign institutional investors (FIIs) bought shares worth a net Rs 648.05 crore on Friday, as per provisional data from the stock exchange.
The Indian benchmark BSE-30 index, Sensex, resumed higher at 19,442.19 and moved up further to 19,478.01, but declined afterwards to 19,393.68 before quoting 19,431.43 points at 1050 hours, still showing a gain of 7.33 points, or 0.04 per cent, from its last weekend's level.
In New York market, the dollar gained versus major currencies on Friday after data showed the US economy added more jobs than expected in November.
The euro came under independent pressure as expectations for interest-rate cuts increased.
