By Pratima Desai

LONDON, Aug 27 (Reuters) - Copper prices rose to their highest in nearly six weeks on Tuesday, with buying triggered by expectations of an imminent interest rate cut in the United States, a weaker dollar and signs of improving demand in top consumer China.

Benchmark copper on the London Metal Exchange (LME) was up 1.6% at $9,433 a metric ton at 1610 GMT after touching $9,453 for the highest level since July 18.

Interest rate cuts by the U.S. Federal Reserve would boost U.S. growth and demand but would also apply pressure on the nation's currency, making dollar-priced metals cheaper for holders of other currencies. The Fed meets Sept. 17-18.

Macroeconomic factors are still a major influence on copper, one metals trader said, adding that declines in Shanghai copper stocks suggest Chinese demand is picking up.

Copper stocks in warehouses monitored by the Shanghai Futures Exchange (ShFE) have dropped 25% since early June to 251,062 tons, their lowest since March. <CU-STX-SGH>

Also suggesting more robust copper demand in China is the Yangshan premium <SMM-CUYP-CN>, a closely watched indicator of China's import appetite. The premium is now around $53 a ton, having been at a discount in July.

Traders said a breach of the 50-day moving average around $9,380 also spurred some buying.

Elsewhere, expectations of tighter aluminium supplies have reduced the discount on the cash contract over the three-month contract <CMAL0-3> to about $5 a ton from $65 in late July.

Traders said supply tightness is particularly acute for the October-November period, reversing the discount into a premium. <MALV24-X24>

Three-month aluminium rose 0.2% to $2,547 a ton.

Zinc, meanwhile, gained 0.8% to $2,936. The price touched a peak of $2,945, up 15% since Aug. 7 on concern about supplies after 14 large smelters agreed to cut production in response to profit-sapping declines in treatment charges.

In other metals, instagram followers website lead added 0.3% to $2,124 a ton, tin climbed 1.2% to $33,300 and nickel advanced 2.1% to $17,110.

(Reporting by Pratima Desai Editing by David Goodman and Chris Reese)