Investors are increasingly hopeful the government will, in its budget on Thursday, announce measures to attract more foreign fund flows into the country.
Net inflows into the country's equity market have been a key determinant of the rupee's fortunes in recent years. Foreigners have so far this year bought $8.4 billion worth of local shares after purchasing $24.55 billion in 2012.
"I expect a positive week for the rupee and think it will appreciate towards 53.50 this week," said Samir Lodha, managing director at QuantArt Market Solutions.
"Pre-budget expectation build-up will help on the domestic front," he added.
The partially convertible unit closed at 53.8650/8750 per dollar, after touching 53.86, its strongest since February 15. The unit had closed at 54.1750/1850 on Friday.
Traders said gains in the domestic sharemarket also helped the rupee. Indian shares ended marginally higher after touching their lowest in 2013 intraday as technology firms such as Infosys gained on hopes the budget would provide incentives to exporters.
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However, continued dollar demand from oil refiners, the largest buyers of dollars in the domestic currency market, to meet month-end import commitments limited further gains in the rupee.
"NDFs have been seeing heavy dollar selling pushing the USD/INR down locally as well. But good demand from oil limited a further downside," a senior dealer with a state-run bank said.
The spot non-deliverable forward was mostly stronger than the onshore spot rate through the session, dealers said. The spot NDF closed at 54.97 while the most-traded one-month NDF ended at 54.26.
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 all closed at around 53.87 with a total traded volume of around $8 billion.