MUMBAI (Reuters) - The rupee was firm in afternoon trades on Tuesday in tandem with the euro's gains and positive local shares, but dollar demand from oil companies limited the rise. * At 1:29 p.m., the partially convertible rupee was at 44.70/71 per dollar, stronger from last close of 44.755/765. * The rupee has so far moved in the 44.700-44.825 range, and is expected to be in 44.70-44.85 band in the remaining trade. * The euro was trading at $1.4660, after touching a low of $1.4564. The unit had been at $1.4607 when the domestic market closed on Monday. * The euro held firm below its one-month high on Tuesday, though further climbs after a two-week rally may require clear signals from the European Central Bank later in the week that it plans to raise interest rates next month. * The index of the dollar against six major currencies was down 0.41 percent at 73.651 points. * Indian shares pared early losses on Tuesday as energy major Reliance Industries climbed, but the market faced headwinds to push ahead after a spate of data showed slowing growth. * Oil is India's biggest import item and domestic oil refiners are largest dollar purchasers in local forex market. (Reporting by Aditya Phatak; Editing by Rajesh Pandathil)