* Canadian dollar strengthens 0.1% against the greenback * Loonie trades in a range of 1.2581 to 1.2627 * Price of U.S. oil falls 0.7% * Canadian bond yields ease across a flatter curve TORONTO, April 8 (Reuters) - The Canadian dollar edged higher against its U.S. counterpart on Thursday, recovering from a one-week low, as data showing an unexpected rise in the number of Americans filing new claims for unemployment benefits weighed on the greenback. The U.S. dollar fell against a basket of major currencies after initial claims for state unemployment benefits totaled a seasonally adjusted 744,000 for the week ended April 3, up from 728,000 in the prior week. The greenback was also pressured by reassurance on Wednesday from the Federal Reserve that its bond-buying support for economic recovery will not be ending anytime soon. The Canadian dollar was trading 0.1% higher at 1.2600 to the greenback, or 79.37 U.S. cents, having traded in a range of 1.2581 to 1.2627. On Wednesday, it touched its weakest intraday level since March 31 at 1.2634. Canada"s employment report for March, due on Friday, could offer clues on the Bank of Canada"s policy outlook. The central bank has become more upbeat about prospects for economic growth, while some strategists expect it to cut bond purchases at its next interest rate announcement on April 21. On a more cautious note for the economy, Ontario, Canada"s most populous province, began a four-week stay-at-home order and closed in-store shopping for non-essential retailers as it battles a third wave of the COVID-19 pandemic. The price of oil, one of Canada"s major exports, fell after official data showed a big increase in U.S. gasoline stocks. U.S. crude oil futures were down 0.7% at $59.33 a barrel. Canadian government bond yields were lower across a flatter curve, with the 10-year down 2.3 basis points at 1.479%. On Wednesday, it touched a nine-day low at 1.460%. (Reporting by Fergal Smith; Editing by Alison Williams)