Aug 11 (Reuters) - Copper prices rose on Thursday to their highest in nearly six weeks, helped by easing demand worries after U.S. inflation data came in softer than expected and some short-covering.

Three-month copper on the London Metal Exchange was up 0.9% to $8,156.50 a tonne at 0701 GMT, while the most-traded August copper contract on the Shanghai Futures Exchange closed 2.2% higher at 62,690 yuan ($9,304.36) a tonne.

Both contracts hit their highest since July 1 earlier in the session.

U.S. consumer prices did not rise in July compared with economists' expectation of a 0.2% gain, an outcome that could allow the Federal Reserve to dial down the size of its interest rate hike in September.

Rising interest rates could curb global economic growth and hurt demand for industrial metals. Copper is often used as a gauge of global economic health.

"The market has been short as per our estimates in which macro fears of inflation were depressing commodities prices," said Zenon Ho, an analyst at broker Marex.

"Yesterday, U.S. data was surprisingly good and there was a certain element of short-covering involved."

However, U.S. policymakers pushed back on market expectation for rate cuts next year and assured they would continue to tighten monetary policy until price pressures are fully broken.

ShFE nickel jumped as much as 6.2% to 178,100 yuan a tonne, zinc closed 2% higher at 25,265 yuan a tonne and tin increased 2.5% to 201,000 yuan a tonne.

Tight inventories across base metals also lent support to prices.

ShFE copper stockpiles were at their lowest since Jan. 21, while LME inventories of the metal fell to their lowest since June 29 and were down 30% since May.

LME nickel stocks have fallen 73% in a year to 56,244 tonnes, the lowest since October 2008.

LME aluminium rose 0.6% to $2,504.50 a tonne and LME nickel advanced 2.1% to $22,960 a tonne.

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($1 = 6.7377 yuan) (Reporting by Mai Nguyen in Hanoi Editing by Subhranshu Sahu and Mark Potter)