* Canadian dollar strengthens 0.1% against the greenback * Canadian building permits fall by 0.5% in April * Price of U.S. oil climbs nearly 1% * Canadian bond yields rise across much of the curve TORONTO, June 2 (Reuters) - The Canadian dollar edged higher against its broadly stronger U.S. counterpart on Wednesday as oil prices climbed, with the currency staying in reach of a six-year high notched the day before. Oil, one of Canada"s major exports, was supported by an OPEC+ decision to stick to its plan to restore supply to the market gradually and by the slow pace of nuclear talks between Iran and the United States. U.S. crude prices rose nearly 1% to $68.37 a barrel, while the Canadian dollar was trading 0.1% higher at 1.2063 to the greenback, or 82.90 U.S. cents. It traded in a range of 1.2057 to 1.20915, having on Tuesday touched its strongest level since May 2015 at 1.2007. The U.S. dollar rebounded from near a five-month trough versus major peers, as a pickup in U.S. manufacturing kept bets alive for a quicker normalization of Federal Reserve policy. Canada"s central bank, which is due to make an interest rate announcement next Wednesday, has already begun cutting the pace of its bond purchases. It is likely to cut further over the coming months, possibly as soon as July, as provinces ease curbs to contain the coronavirus pandemic and inflation pressures build, analysts said. The value of Canadian building permits fell by 0.5% in April after rising by a record in March, Statistics Canada said. Canada"s jobs report for May is due on Friday. Canadian government bond yields edged higher across much of the curve, with the 10-year up 1.1 basis points at 1.503%. (Reporting by Fergal Smith Editing by David Holmes) Our Standards: The Thomson Reuters Trust Principles.