June 10 (Reuters) - Most non-ferrous metals prices fell on Monday, with London copper hitting its lowest in more than five weeks, amid a firm dollar and constraints in physical demand.

Three-month copper on the London Metal Exchange fell 0.2% to $9,747 per metric ton by 0417 GMT, aluminium shed 1% to $2,552.50, zinc dropped 0.9% to $2,741 and lead eased 0.4% to $2,190.50.

LME tin edged down 0.1% at $31,410 a ton, and nickel was nearly unchanged at $18,035.

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.

Earlier in the session copper prices fell 0.2% to $9,741 a ton, their lowest since May 2. 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.

Copper inventories in warehouses tracked by the Shanghai Futures Exchange 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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0830 EU Sentix Index June

(Reporting by Mai Nguyen in Hanoi; Editing by Eileen Soreng)