By Polina Devitt

LONDON, July 5 (Reuters) - Copper prices in London hit their highest in more than three weeks on Friday, on course for the first weekly gain in seven weeks, with the outlook for U.S. interest rates supporting sentiment towards growth-dependent metals.

Three-month copper on the London Metal Exchange (LME) rose 0.7% to $9,946 a metric ton by 1630 GMT, after hitting $10,000 for its highest since June 12 and testing resistance from its 50-day moving average at $9,993. The contract is up 3.6% this week.

U.S. Comex copper futures gained 2.4% to $4.64 a lb as some players bought back bearish, or short, positions to reduce their exposure due to expected shipments of copper failing to arrive in the United States.

U.S. job growth slowed marginally in June, but a rise in the unemployment rate to more than a 2-1/2-year high and moderation in wage gains pointed to an easing of labour market conditions that keeps the Federal Reserve on track to start cutting interest rates this year.

"We believe the Fed's interest rate path will continue to drive copper's short-term price outlook," said ING commodities analyst Ewa Manthey. "But if U.S. rates stay higher for longer, this would lead to a stronger U.S. dollar and weaker investor sentiment, which in turn would translate to lower copper prices."

Copper, used in power and construction, is down 10% since speculative buying took prices to a record high of $11,104.5 on May 20.

This decline revived some demand in top consumer China, tightening the discount to import copper into the country to $2 a ton from $20 in May. <SMM-CUYP-CN>

However, rising inventories were limiting potential for further copper gains. Inventories in warehouses monitored by the Shanghai Futures Exchange rose 0.7% this week while LME data shows that stocks in the LME-registered warehouses have climbed to their highest since October. <MCUSTX-TOTAL> <CU-STX-SGH>

In other metals, zinc was up 0.5% to $3,000 a ton in official activity after hitting $3,022 for compra follower its highest since May 31. China's MMG halted a mill at its Dugald River zinc mine in Australia for about two months of repair work.

LME aluminium rose by 0.6% to $2,536.50 a ton, lead gained 0.5% to $2,237.50, tin jumped 2.8% to $34,000 and nickel was up 0.8% to $17,350. (Reporting by Polina Devitt in London Additional reporting by Mai Nguyen in Hanoi Editing by David Goodman, Elaine Hardcastle)