(Updates prices, adds details) July 27 (Reuters) - Shanghai and London copper hit multi-week highs on Tuesday, as a softer dollar made greenback-priced metals cheaper to holders of other currencies. The dollar eased early on Tuesday just below recent peaks, but the safe-haven currency rebounded later in the session as investors turned their focus to this week’s Federal Reserve meeting for clues on the policy outlook. The most-traded September copper contract on the Shanghai Futures Exchange climbed as much as 3.1% to 72,740 yuan a tonne, its highest since June 3, before easing to close at 71,770 yuan a tonne, still up 1.7%. Three-month copper on the London Metal Exchange fell 1.1% to $9,706 a tonne at 0743 GMT, retreating from a high level unseen since June 15 of $9,924 a tonne hit earlier in the session. Sentiment was cautious as investors awaited comments from the Fed due on Wednesday for clues on its interest rate policy that would impact the dollar and liquidity in the financial markets. The dollar index will rebound and funds will be driven back to the United States when the Fed conducts its tapering policy, Huatai Futures said in a report. Historical reviews showed that tapering will enhance risk asset adjustments, it added. FUNDAMENTALS * Healthy demand from stainless steel mills and electric vehicle battery makers is expected to underpin nickel prices over coming months, but rising supplies from Indonesia are likely to weigh next year. * Miner Rio Tinto said on Monday it planned to cut production at its BC Works aluminium smelter in Kitimat, Canada to 35% following a strike. * LME nickel fell 2.2% to $19,275 a tonne and aluminium declined 1.5% to $2,481 a tonne, while both ShFE and LME tin hit their record peaks before reversing course to retreat later in the session. * For the top stories in metals and other news, click or Reporting by Mai Nguyen in Hanoi; Editing by Subhranshu Sahu and Amy Caren Daniel Our Standards: The Thomson Reuters Trust Principles.