TOKYO, July 12 (Reuters) - Japanese government bond (JGB) yields declined on Friday, tracking their U.S. peers down after key inflation data from the world's largest economy came in cooler than expected, boosting hopes of an interest rate cut in September.

At the same time, the market remained divided over the possibility of a July rate hike in Japan amid speculation and local media reports that Tokyo may have intervened in the currency market yet again.

The 10-year JGB yield fell 2 basis points (bps) to 1.06%, while 10-year JGB futures rose 0.18 yen to 143 yen.

U.S. Treasury yields dropped on Thursday after data showed consumer prices slipped last month, reinforcing expectations the Federal Reserve will start cutting rates in September.

The slide supported buying of JGBs, which tend to move in tandem with their U.S. peers.

But the sudden appreciation of the yen away from 38-year lows after the data had concerns about Japan's monetary policy path top of mind.

"I think the market is having a little bit of a hard time digesting the news because they can see (how it could impact the BOJ's decision) both ways," said Naka Matsuzawa, chief macro strategist at Nomura Securities.

Investors have debated whether the Bank of Japan will raise rates this month, at the same meeting it plans to unveil JGB purchase tapering details. Some market players bet yen weakness could give the bank another incentive to hike.

A now somewhat stronger yen could take a little heat off the BOJ, but if Japanese authorities have in fact had to step in again, the central bank may face pressure to support the currency, perhaps even by raising rates, said Matsuzawa.

The two-year JGB yield had yet to trade as of 0320 GMT.

The five-year yield fell 1.5 bps to 0.59%.

The 20-year JGB yield tumbled 2 bps to 1.89%.

The 30-year JGB yield was 3.5 bps lower at 2.19%.

(Reporting by Brigid Riley; Editing by Mrigank Dhaniwala)