Dec 12 (Reuters) - The Indian rupee was weak in afternoon trade on Monday dragged by soft local shares after bleak factory output data deepened growth concerns, though likely dollar sales by some nationalised banks helped rupee recover some losses, traders said. * At 2:07 p.m., the partially convertible rupee was at 52.52/53 per dollar, weaker than Friday's close of 52.03/04, but stronger from the day's low of 52.66 -- near the record low of 52.73 touched Nov. 22. * Traders said any big recovery in the rupee may be hampered by dollar demand from oil importers, the largest purchasers of the greenback in local forex market, and a weak euro. * The euro slipped in Asia on Monday, and was expected to struggle going into the year-end after the European Union agreed on deeper economic integration but fell short of a convincing plan to deal a decisive blow to the region's debt woes. * India's main share index was down 1.4 percent after government data showed the country's industrial output in October contracted 5.1 percent, a much sharper-than-expected drop. (Reporting by Aditya Phatak; Editing by Harish Nambiar)

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