MUMBAI, Dec 10 (Reuters) - The Indian rupee recovered from the day's lows on Thursday afternoon tracking gains in the local sharemarket but the dollar's rise against major units and demand for the U.S. unit from oil refiners continued to weigh. * At 3:45 p.m., the partially convertible rupee INR=IN was at 46.62/63 per dollar, off a low of 46.73 but still weaker than its close of 46.535/545 on Wednesday when it dropped to 46.87 during trade, its weakest since Nov. 27. * The index of the dollar .DXY against six majors was down 0.1 percent. * Dealers said dollar demand from oil firms was also weighing on the rupee, but gains in the sharemarket helped it recover from the lows. Indian shares .BSESN were trading 0.4 percent higher. [.BO] * The Reserve Bank of India (RBI) said it would withdraw from Jan. 1 some concessions on overseas borrowing for Indian firms introduced during the global credit crisis, although it also eased rules for the infrastructure and telecoms sectors. [ID:nBOM311662] * In the currency futures market INRFUTURES, the most traded near-month contracts on the National Stock Exchange and MCX-SX were both quoting at 46.6950 respectively, with the total traded volume on the two exchanges at about $3.9 billion. (Reporting by Swati Bhat; Editing by Sunil Nair)

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