* Canadian dollar strengthens 0.3% against the greenback * Canadian GDP rises 5.6% annualized in the first quarter * Price of U.S. oil increases 3.4% * Canadian bond yields climb across a steeper curve By Fergal Smith TORONTO, June 1 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Tuesday, moving close to a recent six-year high, as oil prices rose ahead of an OPEC supply decision and data showed first quarter growth in the domestic economy. The loonie , which has benefited this year from higher commodity prices and a more hawkish stance from the Bank of Canada, rose 0.3% to 1.2031 per greenback, or 83.12 U.S. cents. Two weeks ago, it touched its strongest level since May 2015 at 1.2014. Canada"s first quarter annualized growth was 5.6%, reflecting continued strength in the economy influenced by favorable mortgage rates, government transfers and stronger employment, Statistics Canada said. Still, a preliminary estimate showed a 0.8% contraction in April, when lockdowns were in place in some provinces to curb a third wave of the COVID-19 pandemic. The data is backward looking and unlikely to have much impact on the Bank of Canada"s outlook for the economy, said Simon Harvey, FX market analyst for Monex Europe and Monex Canada. Instead, the central bank will be "looking at what OPEC decides later today and what the signal is for the price of oil for the remainder of the year," Harvey said. The Organization of the Petroleum Exporting Countries (OPEC) and its allies are likely to agree to continue a slow easing of supply curbs when they meet on Tuesday, OPEC sources said. U.S. crude prices were up 3.4% at $68.6 a barrel, while the U.S. dollar fell against a basket of major currencies and global stocks hit a record high as investors shrugged off concerns about rising inflation. Canadian government bond yields were higher across a steeper curve, tracking a move in U.S. Treasuries. The 10-year rose 4.3 basis points to 1.526%. (Reporting by Fergal Smith; Editing by Steve Orlofsky) Our Standards: The Thomson Reuters Trust Principles.