SYDNEY, Jan 9 (Reuters) - Australia"s most populous state, New South Wales, recorded its highest number of daily COVID-19 deaths on Saturday as the Omicron variant sweeps the country and lawmakers face pressure to close widening supply chain gaps. The home to Sydney and a third of Australia"s 25 million people reported 16 deaths from the coronavirus in the previous day. New South Wales reported 30,062 new infections, near record levels. The second-largest state, Victoria, which hosts the Australian Open tennis tournament this month, reported 44,155 new COVID-19 cases and four deaths. The country reported just under 100,000 cases overall, down from a record 116,025 the previous day, but still surpassing most previous peaks. Total deaths for the day were 36. With the surge bringing a rush for government-funded pop-up testing clinics, the authorities have shifted their messaging and urged people to instead take rapid antigen tests at home, then report positive results to their doctor, who enters it into a database. Authorities are calling for calm amid reports of bare supermarket shelves as people stay home to avoid infection and delivery personnel self-isolate due to virus exposure. "We have seen very low rates of significant illness," federal Health Minister Greg Hunt told reporters. "It is the workforce furloughing which remains the principal challenge at this point in time." The government and its health advisers have cut mandatory isolation times for close contacts and narrowed the definition of close contacts but were still reviewing the rules for furloughing workers, Hunt said. Australia meanwhile plans to start vaccinating children aged 5 to 11 on Monday. Most states said they would begin the new school year as scheduled at the end of January but Queensland, the third most populous state, said it would postpone the return to school by two weeks to give children time to be vaccinated. Despite the outbreak, political leaders have cited Australia"s high vaccination rate - more than 90% of people over 16 are fully vaccinated - to justify a reopening plan. But several states in recent days have postponed non-urgent elective surgery to clear hospital beds for COVID-19 patients and reintroduced mask mandates. New South Wales, which emerged from more than 100 days of lockdown late last year, has reinstated a ban on dancing and drinking while standing up in bars.