* Canadian dollar strengthens 0.2% against the greenback * Canada"s trade surplus narrows to C$778 million in July * Price of U.S. oil rises 2% * Canada"s 10-year yield unchanged at 1.181% By Fergal Smith TORONTO, Sept 2 (Reuters) - The Canadian dollar edged higher against its U.S. counterpart on Thursday as higher oil prices offset data showing that Canada"s trade surplus narrowed in July. The price of oil, one of Canada"s major exports, was supported by a sharp decline in U.S. crude stocks and a weaker U.S. dollar, though gains were capped by an OPEC+ decision to stick to its policy of gradually increasing output. U.S. crude oil futures rose 2% to $69.99 a barrel, while the Canadian dollar was trading 0.2% higher at 1.2594 to the greenback, or 79.40 U.S. cents. The currency traded in a range of 1.2587 to 1.2638. Canada"s trade surplus narrowed to C$778 million in July from a revised C$2.6 billion in June, as imports rose at a faster pace than exports, Statistics Canada data showed. After stripping away price effects, exports fell 0.3%, which disappointed some economists. "Add today"s international trade report to the list of recent negative economic surprises suggesting that the Canadian economy hit a soft patch in the beginning of the third quarter," said Omar Abdelrahman, an economist at TD Economics. Data on Tuesday showed that Canada"s economy shrank at an annualized rate of 1.1% in the second quarter and likely had far less momentum than had been expected heading into the summer. Investors awaited U.S. jobs figures on Friday for clues on the timing of the Federal Reserve"s stimulus taper. The Bank of Canada is due to make an interest rate decision next week. Canadian government bond yields were mixed across the curve, with the 10-year unchanged at 1.181%. (Reporting by Fergal Smith; editing by Jonathan Oatis) Our Standards: The Thomson Reuters Trust Principles.