LONDON - Copper prices rose on Tuesday, helped by low inventories, signs of improving demand in China and fears that sky-high energy prices could force smelters to cut output.

Investors remained cautious, however, with a global economic slowdown threatening to curtail demand.

Prices are up 16% from a low in mid-July, but they are still down 17% since the start of the year and have largely flatlined in recent weeks.

In official trading on Tuesday benchmark copper on the London Metal Exchange (LME) was up 0.3% at $8,050 a tonne.

Prices have held steady despite the U.S. dollar reaching close to 20-year highs, which makes metals costlier for buyers with other currencies, and falling global stock markets.

"Most of the selling has been done by now," said Saxo Bank analyst Ole Hansen, pointing to data that shows speculators have already adopted bearish positions.

Copper should rise to about $9,000 a tonne by the end of the year, he said.

High energy costs mean that without state support or price hedges, copper smelters in Europe would face losses of $2.7 billion, analysts at Bank of America said.

High power costs have already prompted temporary shutdowns at aluminium and zinc smelters in Europe.

Data on Tuesday showed that manufacturing has contracted in Europe this month and factory activity growth in Japan slowed.

But China, the biggest metals consumer, this week cut its benchmark lending rate and has moved to support its property market.

Yangshan copper import premiums reached a 10-month high of $112.50 on Friday and inventories in Shanghai Futures Exchange (ShFE) warehouses are near 13-year lows at 31,205 tonnes.

On-warrant inventories on the LME have also fallen to 72,250 tonnes from 121,200 tonnes at the start of July.

The premium on the LME for cash copper over the three-month contract has risen to about $60, suggesting tighter supply.

LME aluminium was up 1.1% at $2,416 a tonne, zinc was down 1.2% at $3,455, nickel slipped 2.2% to $21,850, lead lost 0.5% to $2,004 and tin was 1.5% down at $24,100.

(Reporting by Peter Hobson, Additional reporting by Siyi Liu and Emily Chow, Editing by David Goodman, Kirsten Donovan)