London June 13 (Reuters) - A rebound in copper prices paused on Thursday as U.S. dollar steadied after Federal Reserve pushed back the interest rate cut to the end of this year.

Three-month copper on the London Metal Exchange (LME) was down 0.7% at $9,877 per metric ton by 1032 GMT.

It surged on Wednesday to above $10,000 after May U.S. inflation came slower than expected, bolstering expectations of earlier rate cuts.

"We had a bullish sentiment after inflation data yesterday but then the Fed statement after LME close suggested that there would only be one cut this year," said Robin Montefusco with Sucden Financial.

Profit taking was seen over the last few weeks, he said, with copper prices likely to be rangebound with a key support level at $9,500.

Dollar steadied after the Fed held interest rates steady on Wednesday. A stronger dollar makes greenback-priced metals costlier for holders of other currencies.

Copper buyers are still not back to the market although prices have retreated 11% from an all-time high in May.

More copper arrived at LME-registered warehouses in Taiwan and South Korea on Thursday, as Chinese producers took advantage of record LME prices in May to export their copper.

LME copper inventory rose 22% to 127,343 tonnes over the past one month.

"Prices will be rangebound until we get better numbers out of China market on the demand narrative," the broker said.

LME aluminum fell 0.5% to $2,563.50 a ton, nickel declined 2% to $17,700, zinc shed 0.7% to $2,874.5, lead rose 0.3% to $2,179, and tin was flat at $33,400. (Reporting by Julian Luk in London; Editing by Mrigank Dhaniwala)