(Adds strategist quotes and details throughout; updates prices) * Canadian dollar strengthens 0.5% against the greenback * Loonie trades in a range of 1.2711 to 1.2791 * Price of U.S. oil settles 1.7% higher * Canada"s 10-year yield touches its highest since March at 0.887% By Fergal Smith TORONTO, Jan 12 (Reuters) - The Canadian dollar strengthened against its U.S. counterpart on Tuesday as oil prices rose and the greenback broadly declined, with the currency rebounding from its weakest in nearly two weeks the day before. The loonie was trading 0.5% higher at 1.2714 to the greenback, or 78.65 U.S. cents, having traded in a range of 1.2711 to 1.2791. On Monday, it touched its weakest since Dec. 29 at 1.2835. The move higher for the loonie was down to the rally in oil and "general market sentiment," said Tony Valente, senior FX dealer at AscendantFX, adding that it"s "a slow news week ahead of next week"s Bank of Canada policy meeting." Money markets see an increased chance of the Bank of Canada cutting interest rates closer to zero, as tightening economic restrictions to contain a second wave of COVID-19 cases offset optimism that activity will rebound later this year. Ontario declared an emergency after the latest modeling put Canada"s most populous province on track to have more than 20,000 new COVID-19 cases per day by the middle of February. Oil, one of Canada"s major exports, rose to its highest since last February as Saudi Arabia"s plans to limit supply offset worries that rising coronavirus cases globally would curtail fuel demand. U.S. crude oil futures settled 1.7% higher at $56.68 a barrel, while the U.S. dollar edged lower against a basket of currencies, as its recent rally, driven by a spike in U.S. Treasury yields, appeared to run out of steam. Canadian government bond yields were mixed across a steeper curve in tandem with U.S. Treasuries. The 10-year was little changed at 0.844%, having touched its highest intraday since March 26 at 0.887%. (Reporting by Fergal Smith; Editing by Kirsten Donovan and Jonathan Oatis)