The government received $7 billion worth of total bids on Monday, the first day of the auction and looked set to top its minimum target of raising $1.8 billion initially.
Foreign companies like Vodafone and Telenor would have to convert their dollars to rupees if they win licences, with the first tranche needing to be paid within 10 days of allocation.
The rupee also benefited as Asian currencies firmed up later in the session on Tuesday as the region is seen better placed than other emerging markets to face the fallout of any global risk aversion due to the U.S. Federal Reserve's stimulus tapering and concerns of a slowdown in China.
"There have been rumours of fund flows related to the mobile spectrum auction over the last two days. The recovery in stocks also helped the rupee," said Uday Bhatt, a senior manager at UCO Bank.
He expects the rupee to trade in a range of 62-63.50 to the dollar in the near term.
The partially convertible rupee closed at 62.5250/5350 per dollar compared with Monday's 62.56/57, after initially falling to a session low of 62.81.
Dealers spotted healthy dollar selling by foreign banks, which they attributed to inflows related to the spectrum sale.
Meanwhile, shares rebounded from four-month lows, also helping the rupee. India's benchmark BSE index ended flat on Tuesday after declining as much as 1.2 percent.
Concerns about selling by foreign investors have clouded the outlook for Indian markets. Overseas funds sold a net $1.7 billion worth of shares and debt over seven sessions to Monday, according to preliminary exchange and regulatory data.
Still, India is seen as less vulnerable than last year when similar fears of a Fed tapering sent the rupee crashing to a record low of 68.85 to the dollar on Aug. 28.
In the offshore non-deliverable forwards, the one-month contract was at 62.95, while the three-month was at 63.84.
* Rupee ends at 62.5250/5350 vs Monday's close of 62.56/57
* Strong demand seen at Indian mobile spectrum sale
* Shares rebound from four-month lows
FACTORS TO WATCH
* Aussie surges after central bank's policy turn
* Emerging stocks at 5-month low; rouble nears 5-year low
* Shares plunge as U.S. slowdown adds to EM woes
* Foreign institutional investor flows