* Canadian dollar was near flat against the greenback * Loonie touches its weakest since last Wednesday at 1.2628 * Price of U.S. oil rises 0.9% * Canadian bond yields were mixed across the curve TORONTO, April 13 (Reuters) - The Canadian dollar was little changed against its U.S. counterpart on Tuesday as oil rose and U.S. data showed a tamer-than-expected increase in U.S. underlying inflation, with the loonie rebounding from an earlier six-day low. The U.S. dollar fell against a basket of major currencies after data showed that U.S. consumer prices increased by the most in more than 8-1/2 years in March but that the core measure was up by just 0.1%, short of analyst estimates of 0.2%. Wall Street steadied near a record high after U.S. federal health agencies recommended pausing the use of Johnson & Johnson"s COVID-19 vaccine, while the price of oil, one of Canada"s major exports, was supported by strong Chinese import data. U.S. crude prices rose 0.9% to $60.22 a barrel. The Canadian dollar was trading nearly unchanged at 1.2564 to the greenback, or 79.59 U.S. cents, having touched its weakest since last Wednesday at 1.2628. Business sentiment in Canada continues to improve and many firms consider the impacts of the COVID-19 pandemic behind them, though the outlook remains challenging for high-contact services, a Bank of Canada survey showed on Monday. The central bank is due to make an interest rate decision next week. Some strategists expect it to cut its bond purchases. Canadian government bond yields were mixed across the curve, with the 10-year little changed at 1.513%. (Reporting by Fergal Smith Editing by Alistair Bell)