SYDNEY, Sept 27 (Reuters) - Australia's New South Wales state, the epicenter of the country's worst coronavirus outbreak, reported on Monday its lowest rise in COVID-19 cases in more than a month as it begins to ease some tough restrictions amid higher vaccinations.

A total of 787 new locally acquired COVID-19 cases were reported, the majority in state capital Sydney, down from 961 a day earlier, according to a statement from the state health department. The state recorded 12 new deaths, taking the total number of fatalities from the latest outbreak to 309. (Reporting by Renju Jose; Editing by Muralikumar Anantharaman)