* Canadian dollar gains 0.3% against the greenback

* Price of U.S. oil settles 0.8% higher

* 10-year yield hits a three-month low

TORONTO, June 12 (Reuters) - The Canadian dollar gave back some earlier gains against its U.S. counterpart on Wednesday as the Federal Reserve signaled a reduced number of interest rate cuts this year despite evidence of cooling inflation.

The loonie was trading 0.3% higher at 1.3710 per U.S. dollar, or 72.94 U.S. cents, after trading in a range of 1.3681 to 1.3760.

The Fed held rates steady

, as expected, with officials projecting only a single quarter-percentage-point reduction for the year compared to three previously.

"Treasury yields are partially reversing this morning’s declines, and the (U.S.) dollar is inching higher, suggesting that market participants are viewing the (rate) decision through a very modestly-hawkish lens," Karl Schamotta, chief market strategist at Corpay, said in a note.

Earlier on Wednesday, data showed U.S. consumer prices cooling more than expected in May, pressuring the greenback against a basket of major currencies.

"For Canada, lower global inflation gives central banks an opportunity to cut rates and stimulate growth which should translate directly into Canadian resources," said Adam Button, chief currency analyst at ForexLive.

"The Canadian dollar is a pro-cyclical currency and rate cuts should kick off a round of global growth in time."

The price of oil, one of Canada's major exports, settled 0.8% higher at $78.50 a barrel, helped by forecasts that global oil inventories would fall in the second half of 2024.

Bank of Canada Governor Tiff Macklem was due to participate in a panel discussion on economic volatility. The central bank will release Macklem's prepared remarks at 3:15 p.m. ET (1915 GMT).

Canadian government bond yields fell across the curve, tracking moves in U.S. Treasuries. The 10-year was down 9.8 basis points at 3.382%, after earlier touching its lowest level since March 12 at 3.354%. (Reporting by Fergal Smith; Editing by Alison Williams and Deepa Babington)