BEIJING, May 22 (Reuters) - Copper prices fell on Wednesday on softening physical demand and higher inventories in top consumer China and as investors were cautious ahead of the release of minutes of the Federal Reserve's latest meeting.

Three-month copper on the London Metal Exchange (LME) was down 1% to $10,750 per metric ton by 0613 GMT.

The most-traded June copper contract on the Shanghai Futures Exchange (SHFE) lost 1.1% to 86,160 yuan ($11,903.35) a ton.

Both contracts had hit record highs on Monday amid copper concentrate supply shortages and demand optimism.

But a lack of fundamental support cooled the rally, which had dampened consumption from copper users, traders said.

Discount to buy copper in China's spot market widened to 340 yuan per ton on Tuesday, the biggest since January 2015, according to Shanghai Metals Market .

Copper warehouse stocks on SHFE stood at 291,020 tons last Friday, more than four times higher than that in the beginning of February. Meanwhile, China's April refined copper output rose on a daily average basis from the prior month, easing concerns of smelters' output cut.

The dollar was steady against a handful of peers on Wednesday, as the market assessed calls for patience from Federal Reserve officials and awaited the publication of Fed minutes for more insight on the central bank's interest rate path.

A stronger dollar makes it more expensive to buy the greenback-priced commodity.

LME aluminium gained 0.2% to $2,732 a ton, nickel dropped 0.4% to $21,215, zinc dipped 0.1% to $3,135, tin decreased 0.1% to $34,300, while lead gained 0.5% to $2,348.50.

SHFE aluminium climbed 0.7% to 21,285 yuan a ton, zinc advanced 0.4% to 24,790 yuan, tin shed 0.2% to 277,120 yuan, lead fell 2% to 18,525 yuan, and nickel was 0.5% lower to 157,010 yuan.

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0600 UK Core CPI YY April

0600 UK CPI YY April

1400 US Existing Home Sales April

1800 US Federal Open Market Committee issues minutes from its meeting of April 30-May 1 ($1 = 7.2383 Chinese yuan renminbi) (Reporting by Siyi Liu and Mei Mei Chu; Editing by Mrigank Dhaniwala)