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Urgent genomic sequencing was under way, NSW Health confirmed early on Sunday.
Fourteen passengers who'd been in the nine southern African countries subject to elevated restrictions arrived on a flight from Doha to Sydney on Saturday evening.
Two of them tested positive on arrival.
Scientists are looking into whether they've been infected by the new Omicron B.1.1.529 variant of concern.
All 14 travellers were transferred to special health accommodation for 14 days of quarantine, under new federal government rules.
Passengers who hadn't been in southern Africa may be considered close contacts and be forced to isolate for 14 days.
Under rules announced by federal Health Minister Greg Hunt on Saturday to address the risk posed by Omicron, all travellers who have recently been in South Africa, Lesotho, Botswana, Zimbabwe, Mozambique, Namibia, Eswatini, Malawi, and the Seychelles must quarantine for two weeks.
NSW has imposed extra measures, with all overseas arrivals ordered to quarantine at home for 72 hours.
Flight crews who have been overseas must isolate for two weeks.
Anyone already in NSW who has been in the nine southern African countries within the previous 14 days must immediately be tested, isolate for 14 days and contact NSW Health.
Premier Dominic Perrottet said precautionary steps were needed to protect against the Omicron variant while experts investigate the risk.
Omicron looked as if it could be even more transmissible than the Delta variant, Health Minister Brad Hazzard said on Saturday.
He said it was concerning for public health officials, though experts were still trying to understand the variant.
Mr Perrottet and Mr Hazzard will address the media on Sunday about the new variant.
Meanwhile, the state added 235 new infections to its caseload on Saturday, and no further deaths.
NSW's hospitals continue to treat 174 patients, 26 of them in intensive care units and 10 requiring ventilation
Testers processed more than 62,000 results in the 24 hours to 8pm on Friday.
NSW is 94.5 per cent single-dosed for everyone 16 and over, while 92.3 per cent are fully vaccinated.
Of 12- to 15-year-olds, 81.2 per cent have received one jab and 76.2 per cent both.
Should NSW reach its goal of 95 per cent full coverage by December 15 an early easing of restrictions will trigger, according to the state's roadmap out of lockdown.