SYDNEY, Sept 8 (Reuters) - New Zealand reported a further fall in locally acquired COVID-19 cases on Wednesday, as the largely coronavirus-free nation looks to eradicate an outbreak of the highly infectious Delta variant. New Zealand reported 15 new locally acquired cases of COVID-19, down from 21 a day earlier, on the first day of an easing of tough restrictions in all regions outside its largest city Auckland. Daily infections hit a peak of 85 on Aug. 29. All of the latest cases were in Auckland. Officials earlier this week said schools, offices and businesses can reopen outside Auckland from Wednesday after near zero cases in the rest of the country, but there will be a cap on gatherings and masks will remain mandatory in public venues. New Zealand had been largely virus-free, excluding a small cluster of cases in February, until an infected traveller from Australia seeded an outbreak, forcing officials to impose a national lockdown last month. About 1.7 million people in Auckland, the epicentre of the outbreak, will be in hard lockdown until at least Sept. 14.