* Canadian dollar gains 0.3% against the greenback

* Touches its strongest since June 25

* Canada posts third straight monthly trade deficit

* Bond yields fall across the curve

TORONTO, July 3 (Reuters) - The Canadian dollar strengthened to its highest level in more than one week against its U.S. counterpart on Wednesday as oil prices rose and economic data added to recent evidence of a slowdown in U.S. activity.

The loonie was trading 0.3% higher at 1.3636 to the U.S. dollar, or 73.34 U.S. cents, after touching its strongest intraday level since June 25 at 1.36175.

"It is more of a U.S. story than a Canadian one," said Tony Valente, senior FX dealer at AscendantFX. "The USD is being pressured by recent U.S. data this morning and the CAD is taking advantage of this."

The U.S. dollar fell against a basket of major currencies as a measure of U.S. services sector activity slumped to a four-year low in June.

Federal Reserve officials at their last meeting acknowledged the U.S. economy appeared to be slowing and that "price pressures were diminishing," but still counseled a wait-and-see approach before committing to interest rate cuts.

The Canadian dollar is set to strengthen over the coming year but its gains will be limited after the Bank of Canada began cutting interest rates ahead of the Fed and as the U.S. election fans economic uncertainty, a Reuters poll found.

Canada recorded a bigger-than-expected trade deficit of C$1.93 billion ($1.41 billion) in May, the third consecutive monthly shortfall, as exports declined faster than imports, data showed on Wednesday.

The price of oil, one of Canada's major exports, settled 1.3% higher at $83.88 a barrel after a larger-than-expected decline in U.S. crude stocks, while Canadian bond yields were down across the curve, tracking moves in U.S. Treasuries.

The 10-year eased 5.4 basis points to 3.555%, pulling back from a one-month high at 3.659% which it touched during Tuesday's session. (Reporting by Fergal Smith; Editing by Josie Kao)