* Canadian dollar falls 0.6% against the greenback * Loonie touches its weakest since last Friday at 1.2114 * Oil touches its highest since October 2018 at $69.40 a barrel * Canadian bond yields rise across much of a steeper curve TORONTO, June 3 (Reuters) - The Canadian dollar weakened to a six-day low against its U.S. counterpart on Thursday, as investors weighed inflation risk and awaited jobs data from both the United States and Canada that could offer clues on central bank policy outlooks. World stock markets stepped back from record highs as rising oil prices added to inflation concerns. Oil , one of Canada"s major exports, rose to its highest level since October 2018 at $69.40 a barrel before dipping below $69. It was supported by expectations for surging fuel demand later this year while major producers maintain supply discipline. The Canadian dollar , which has been on a tear this year due to higher commodity prices and the Bank of Canada"s more hawkish stance, was trading 0.6% lower at 1.2106 to the greenback, or 82.60 U.S. cents. It touched its weakest intraday level since last Friday at 1.2114. The U.S. and Canadian employment reports for May are due on Friday. Economists expect Canadian employment to fall by 20,000 in May after plunging 207,000 in April. Some provinces went into lockdown in April to curb a harsh third wave of the COVID-19 pandemic. Still, the Bank of Canada is seen tapering its asset purchase program again next quarter and raising interest rates earlier than previously predicted amid expectations for a robust economic recovery after a recent downturn, a Reuters poll showed. The U.S. dollar gained ground against a basket of major currencies as a strong U.S. economic rebound threatened to derail the assumption that interest rates will stay low for a long time. Canadian government bond yields were higher across much of a steeper curve, tracking the move in U.S. Treasuries. The 10-year was up 1.3 basis points at 1.508%. (Reporting by Fergal Smith; editing by Jonathan Oatis) Our Standards: The Thomson Reuters Trust Principles.