June 10 (Reuters) - Most non-ferrous metals prices largely fell on Monday, with London copper hitting its lowest in more than five weeks, as better-than-expected U.S. jobs data reduced the chance of rate cuts.

Three-month copper on the London Metal Exchange edged up 0.4% at $9,802 per metric ton by 0755 GMT, but the contract fell as much as 0.2% to $9,741 earlier in the session.

LME aluminium shed 0.4% to $2,567.50, lead eased 0.8% to $2,183, nickel fell 0.3% to $17,985, while zinc rose 0.2% to $2,772 and tin was nearly unchanged at $31,450.

The dollar index rose on Monday, making greenback-priced metals more expensive to holders of other currencies, after U.S. data showed the world's largest economy created a lot more jobs than expected in May.

The jobs data led traders to once again shift their expectations of when the Fed will cut rates and by how much.

"China is out for Dragon Boat (festival), so there was no buying offset on Friday evening, and the NFP (jobs data) just caused macro traders to sell risk assets, including copper, lower," said a trader, expecting prices to rebound when the Chinese are back from holiday.

The LME three-month contract has lost about 12% since it hit a record high of $11,104.50 on May 20 as speculative investors reviewed copper's red-hot rally.

Speculative net positioning on COMEX copper declined to its lowest since April 16 on Tuesday, the latest exchange data showed.

Meanwhile, the usual premium to import copper into China remained at a discount, reflecting weak demand from the world's biggest copper consumer amid high and volatile prices. <SMM-CUYP-CN>

Copper inventories in warehouses tracked by the Shanghai Futures Exchange <CU-STX-SGH> continued to climb and were at 336,964 tons on Friday, the highest since March 2020.

Trading volume was thin due to a public holiday in China. The SHFE is closed on Monday.

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(Reporting by Mai Nguyen in Hanoi; Editing by Eileen Soreng tiktok like and followers Mrigank Dhaniwala)