* Canadian dollar weakens 0.2% against the greenback

* Trades in a range of 1.3715 to 1.3763

* Price of U.S. oil settles 0.15% higher

* 10-year yield hits a 3-month low at 3.321%

TORONTO, June 13 (Reuters) - The Canadian dollar weakened against its U.S. counterpart on Thursday as the greenback notched gains against a basket of major currencies and the Bank of Canada reiterated it could cut interest rates further.

The loonie was trading 0.2% lower at 1.3750 to the U.S. dollar, or 72.73 U.S. cents, after trading in a range of 1.3715 to 1.3763.

"The U.S. dollar has maintained its bid tone since last week's stronger-than-expected nonfarm payrolls report," said Michael Goshko, senior market analyst at Convera Canada ULC.

The U.S. dollar rose after the Federal Reserve on Wednesday pushed out the start of interest rate cuts to perhaps as late as December and despite a soft U.S. producer price inflation report for May that added to recent downward pressure on U.S. Treasury yields.

Data on Friday showed the U.S. economy created far more jobs than expected in May. Also last week, the BoC became the first G7 central bank to cut interest rates.

Speaking to a conference in Ottawa on Thursday, BoC Deputy Governor Sharon Kozicki stuck to the central bank's messaging that further cuts would follow if inflation continued to ease, but the policy decisions would be taken one meeting at a time.

Money markets see a 55% chance of a rate cut at the BoC's next policy decision on July 24.

The price of oil, one of Canada's major exports, settled 0.15% higher at $78.62 a barrel, while Canadian government bond yields moved lower across the curve, tracking moves in U.S. Treasuries.

The 10-year was down 5.5 basis points at 3.337%, after earlier touching its lowest level since March 11 at 3.321%. (Reporting by Fergal Smith; Editing by Paul Simao)