* Canadian dollar gains 0.1% against greenback

* Touches near a two-month low at 1.3791

* Price of U.S. oil settles 0.2% higher

* Bond yields fall across flatter curve

TORONTO, June 11 (Reuters) - The Canadian dollar edged higher against its U.S. counterpart on Tuesday but was trading not far off its weakest level in nearly two months, as oil prices rose and investors awaited a Federal Reserve interest rate decision.

The loonie was trading 0.1% higher at 1.3750 to the U.S. dollar, or 72.73 U.S. cents, after touching its weakest intraday level since April 19 at 1.3791.

"We are seeing the U.S. dollar strengthen as people are concerned that the Fed may not be able to cut interest rates in the near future," said Darren Richardson, chief operating officer at Richardson International Currency Exchange Inc.

The U.S. dollar hit a four-week high ahead of a highly anticipated U.S. inflation report on Wednesday that is likely to influence the timing of the first Fed rate cut.

The U.S. central bank is expected to leave interest rates unchanged at the conclusion of a two-day policy meeting on Wednesday.

The inflation data and the Fed rate decision will be "extremely important" for the performance of the Canadian dollar against the greenback over the coming months, Richardson said.

Last Wednesday, the Bank of Canada became the first G7 central bank to cut rates. BoC Governor Tiff Macklem is due to participate in a panel discussion on economic volatility on Wednesday.

The price of oil, one of Canada's major exports, settled 0.2% higher at $77.90 a barrel as the U.S. EIA raised its world oil demand growth forecast for the year.

Canadian bond yields moved lower across a flatter curve as U.S. yields fell. The 10-year was down 3.1 basis points at 3.475%. (Reporting by Fergal Smith; Editing by Paul Simao)