The rupee closed at 82.89 against the U.S. dollar, 0.06% higher that its previous closing at 82.9375.
The dollar index was slightly lower at 103.8, while most Asian currencies weakened, with the Philippine peso down 0.3% and leading losses.
The dollar-rupee pair continues to see dip-buying demand on moves towards 82.85-82.80, a foreign exchange trader at a foreign bank said.
State-run banks were seen bidding for dollars on Monday, likely on behalf of importer clients, the trader added.
Dollar demand from importers and likely intervention from the Reserve Bank of India have kept the rupee in a tight range over the last few trading sessions.
The central bank bought dollars regularly through last week to prevent the currency from appreciating much amid persistent inflows, traders said.
For now, the rupee's range between 82.80 and 83.10 "remains intact," Gaurang Somaiya, a foreign exchange research analyst at Motilal Oswal Financial Services said.
Meanwhile, the RBI has eased restrictions on banks' arbitrage trades between the outright foreign exchange over-the-counter (OTC) and the non-deliverable forward (NDF) markets, Reuters reported earlier in the day.
Over the week, remarks from several Federal Reserve officials will be key, alongside the release of U.S. core personal consumption expenditures inflation data, the central bank's preferred measure of inflation, due on Thursday.
India will also report its GDP numbers for the October-December quarter later in the week.
(Reporting by Jaspreet Kalra; Editing by Dhanya Ann Thoppil)
By Jaspreet Kalra
