The partially convertible rupee ended at 45.13/14 per dollar, 0.1 percent stronger than its previous close of 45.18/19. It had moved in a range of 45.0500-45.1475 intra-day.
The euro was at $1.4125, firmer than Thursday's close of $1.4016.
"The rupee will continue to be rangy in the near term. I largely see it in a range of 45.00-45.50," said Ashtosh Raina, head of foreign exchange trading at HDFC Bank in Mumbai.
"There are inflows in the market that is supporting the rupee, but dollar demand from oil importers is also high," he said.
Oil is India's biggest import item and domestic oil refiners are largest dollar purchasers in the local currency market.
Oil rose more than $2 a barrel on Friday after the United Nations approved military action to contain Libyan leader Muammar Gaddafi, heightening geopolitical tensions in the oil-rich Middle East, but later turned negative after China raised reserve rate requirements.
Indian shares declined for a second week in a row, shedding 1.5 percent on Friday.
The one-month onshore forward premium was at 33.50 points, higher than 31.00 on Thursday, while the three-month premium rose to 83.25 points from 83.00 and the one-year climbed to 288.50 points from 284.50.
The one-month offshore non-deliverable forward contracts were quoted at 45.46, weaker than the onshore spot rate.
In the currency futures market, the most traded near-month dollar-rupee contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange were all at 45.2075, with the total traded volume at about $7.34 billion.