(Updates prices) Sept 29 (Reuters) - Copper prices advanced on Tuesday, though gains were capped as a steady U.S. dollar made greenback-priced metals less attractive to holders of other currencies. Three-month copper on the London Metal Exchange was up 0.1% at $6,576 a tonne by 0703 GMT, easing from 0.8% touched early in the day. The most-traded November copper contract on the Shanghai Futures Exchange edged up 0.1% to 50,940 yuan ($7,471.73) a tonne. “LME copper opened higher due to Comex prices extending gains even after the LME closed, but LME copper has been giving up (some of) the gains. There’s some U.S. dollar tightness this morning,” said a metals trader based in Singapore. “The (steady U.S. dollar) trend should continue until tomorrow. In October, we get no liquidity, so I think we would still see many people squaring out their positions prior to October,” said the trader, referring to the Oct. 1-8 National Day holiday in China. The dollar was steady against a basket of currencies on Tuesday as traders looked out to the first U.S. presidential debate and developments on the U.S. stimulus bill. FUNDAMENTALS * LME aluminium rose 0.1% to $1,776.50 a tonne, while lead increased 1.1% to $1,854 a tonne. ShFE aluminium climbed 1.7% to 14,205 yuan a tonne and lead advanced 2.3% to 15,200 yuan a tonne. * LME copper stocks MCUSTX-TOTAL rose to their highest since Aug. 20 at 103,125 tonnes. “The players who removed copper from Europe, hedged the flat price and carried the short to end-September, are now struggling to justify paying backs to move the position, hence, they are putting them back into system. I think we should still see 35,000-40,000 tonnes of copper delivered this week,” the trader added. * For the top stories in metals and other news, click or