July 27 (Reuters) - Shanghai and London copper jumped on Tuesday to multi-week highs, as a softer dollar made greenback-priced metals cheaper to holders of other currencies.

The dollar eased, hovering just below recent peaks, 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.

Three-month copper on the London Metal Exchange hit a high of $9,924 a tonne, a level unseen since June 15.

FUNDAMENTALS

* Labor contract negotiation at Chile's Escondida mine, the world's largest copper deposit, entered into a critical phase on Monday with the delivery of a final offer by operator BHP , according to an internal memo sent by the company to workers and seen by Reuters.

* Healthy demand from stainless steel mills and electric vehicle battery makers is expected to underpin nickel prices over coming months, but rising supplies from top producer 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 initiated by the Canadian union Unifor after negotiation talks failed.

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MARKETS NEWS

* Asia's stock markets fell to fresh troughs led by a third straight session of heavy selling in Chinese internet giants, while bond and currency markets traded on edge ahead of the Federal Reserve policy meeting.

DATA/EVENTS (GMT)

1230 US Durable Goods June

1400 US Consumer Confidence July

-- US U.S. Federal Open Market Committee starts its two-

day meeting on interest rates (Reporting by Mai Nguyen in Hanoi; Editing by Subhranshu Sahu)