LONDON, June 28 (Reuters) - Copper prices rose on Friday ahead of U.S. inflation data that could support future rate cuts and as some traders bought futures after they failed to break below key support.

Three-month copper on the London Metal Exchange was up 1.2% at $9,628 per metric ton by 1000 GMT. The contract has fallen 4.4% in June and is set for a sixth straight weekly loss. "The push and pull of the base metals market right now is almost hyper-sensitive to the rate cut outlook," said Nitesh Shah, commodity strategist at WisdomTree.

"The ECB and Switzerland have already cut and the question is when will there be enough cooling of inflation for the Fed to make its move. The data we've been getting seem to be supportive, so rate cuts could be relatively soon."

The Federal Reserve's preferred inflation measure, the personal consumption expenditures (PCE) index, is due at 1230 GMT.

If annual growth slowed to 2.6% in May, as economists expect, it may open the way to interest rate cuts later this year.

There was also buying of copper after it held above a key support level of $9,480 on Thursday, a trader said. A break below that could open up more losses to around $9,100.

After advancing to a record high of $11,104.50 on May 20, copper prices have fallen 14%, partly on sluggish economic data from China and uncertainty over U.S. interest rates.

"I think we will see copper average around $9,500 per ton for the year, but prices will likely go above $10,500 by the year-end, when I suspect we have the first U.S. rate cut," said StoneX analyst Natalie Scott-Gray.

LME zinc added 1.1% to $2,963, having pared gains after LME data showed a 9% rebound in inventories to the highest in nearly three months.

In other metals, LME aluminium gained 1.6% to $2,531.50 a ton, nickel advanced 1% to $17,280, lead rose 0.8% to $2,197 and tin climbed 3.2% to $33,225.

For the top stories in metals, click or ($1 = 7.2672 Chinese yuan) (Reporting by Eric Onstad Additional reporting by Ashitha Shivaprasad in Bengaluru Editing by Emelia Sithole-Matarise)