* Canadian dollar strengthens 0.7% against the greenback * Touches strongest level since Sept. 7 at 1.2561 * Price of U.S. oil increases 3% * Canadian bond yields rise across a steeper curve TORONTO, Oct 4 (Reuters) - The Canadian dollar on Monday strengthened to its highest level in nearly four weeks against its U.S. counterpart as the price of oil, one of Canada"s major exports, rose and the greenback gave back some recent gains against major rivals. Oil advanced as sources said that OPEC and its allies have agreed to stick to their existing output agreement despite pressure from consumers to cool a red hot market. U.S. crude prices were up 3% at $78.19 a barrel, while the U.S. dollar declined against a basket of currencies. Losses for the greenback came after four consecutive weeks of increases. The Canadian dollar was last trading 0.7% higher at 1.2565 to the greenback, or 79.59 U.S. cents, after touching its strongest level since Sept. 7 at 1.2561. Speculators have cut their bearish bets on the Canadian dollar, data from the U.S. Commodity Futures Trading Commission showed on Friday. As of Sept. 28, net short positions had fallen to 20,235 contracts from 27,877 in the prior week. Domestic data showed that the value of building permits decreased 2.1% in August from July. Still, permits were up 16.9% from August last year. Canadian trade data for August is due on Tuesday and the September employment report is due on Friday, which could offer clues on the Bank of Canada"s policy outlook. Canadian government bond yields were higher across a steeper curve, with the 10-year up 4.2 basis points at 1.513%. On Friday, Canada"s 10-year yield moved above its U.S. equivalent for the first time since April last year. (Reporting by Fergal Smith; Editing by Emelia Sithole-Matarise) Our Standards: The Thomson Reuters Trust Principles.