Although the rupee is well above its all-time trough of 68.85 hit on Aug 28, the currency is still down 11.2 percent in 2013, making it Asia's worst performer after the Indonesian rupiah and the Japanese yen.
Traders say the outlook for the rupee has improved on the back of a sharp narrowing in the current account deficit after government and central bank emergency measures such as curbing gold imports.
However, the country's weak growth and high inflation remain concerns ahead of general elections due by May, while traders said they would continue to monitor winding down of U.S. Federal Reserve's monetary stimulus.
"The rupee's outlook looks bright in 2014. Indian markets have withstood the tapering by the Federal Reserve. However, some risks remain on account of more aggressive tapering in the next year and the outcome of the general elections," said Param Sarma, chief executive at NSP Forex.
The partially convertible rupee closed at 61.91/92 per dollar compared with 61.85/86 on Friday.
Large dollar buying, primarily by a big state-run bank, kept the rupee weak on Monday, with faltering domestic shares adding to the weakness.
Markets showed a muted reaction after Reserve Bank of India governor Raghuram Rajan, in a central bank report released on Monday, reiterated the challenge of containing inflation is limiting the central bank's ability to boost economic growth.
However, the rupee rebounded in late session after the foreign investment regulator cleared Vodafone's $1.6 billion investment in its India unit and Tesco's $110 million investment plan.
Concerns about the current account deficit have waned substantially, in part on the back of strong foreign investor inflows into stocks and, lately, bonds.
Net inflows into debt markets reached $872.3 million in December, the first month of purchases by foreign investors since May. Foreign institutional investors have been buyers for seven consecutive sessions in Indian equities, taking their total to $20.1 billion so far this year, regulatory and exchange data showed.
In the offshore non-deliverable forwards, the one-month contract was at 62.49, while the three-month was at 63.31.