SYDNEY, Aug 9 (Reuters) - Australia expanded a COVID-19 lockdown to a rural town and the coastal region of Byron Bay on Monday, as fears grew that the virus has spread from Sydney to the northern tip of the country"s most populous state. Tamworth, a farming town 414 km (257 miles) northwest of Sydney, and Byron Bay, a tourist spot about 770 km north of Sydney, will both enter a seven-day lockdown, New South Wales Premier Gladys Berejiklian said. Neither Tamworth nor Byron Bay has yet recorded a COVID-19 case, but Berejiklian said two infected people had contravened travel bans and travelled there. "As a precaution, the health experts have recommended we lock down Tamworth for one week," Berejiklian told reporters. New South Wales reported 283 locally acquired cases of COVID-19 in the past 24 hours, up from 262 cases a day earlier. The state has struggled to contain a surge of the highly infectious Delta variant despite a lockdown of Sydney now in its seventh week. Neighbouring Victoria state said it would ease restrictions after reporting 11 new COVID-19 cases, the same as the previous day. The majority of the new cases in Victoria spent time in the community while infectious but state Premier Daniel Andrews said the lockdown of areas outside the state capital of Melbourne would be lifted on Monday. Melbourne would remain in lockdown - for the sixth time since the pandemic begun - until at least Aug. 12. read more In Brisbane, capital of Queensland, authorities reported four new local cases on Monday, the first day after the city came out of stay-at-home restrictions. Prime Minister Scott Morrison is under fire for a sluggish vaccine rollout, with only 22% of Australians above 16 fully vaccinated. An opinion poll by the Australian newspaper showed his public approval rating had hit its lowest since the pandemic began. read more Morrison acknowledged mounting frustrations but urged people to be patient. "I know they"re sick of it, I know they"re angry and I know they want it to stop and for life to get back to where they knew it," Morrison told reporters in Canberra. "But there can be no short cuts." Australia has reported about 36,250 cases and 939 deaths, including a woman in her 90s whose death in Sydney was reported on Monday. Morrison has said all Australians over 16 will be offered a vaccine by the end of the year, with prospects for achieving that boosted on Monday when the pharmaceutical regulator gave provisional approval for the Moderna (MRNA.O) shot.