Australia on Wednesday reopened borders to vaccinated skilled migrants and foreign students after a nearly two-year ban on their entry, in a bid to boost an economy hit by stop-start Covid-19 lockdowns.

The emergence of the new Omicron variant forced officials to delay the reopening of international travel by two weeks after health officials sought a pause to get more information about the strain, which appears to show milder symptoms than other coronavirus variants.

"I just met my mum for the first time in four years, I'm so happy and thankful borders have opened," Kang Jin, a traveller from South Korea, told reporters in Sydney.

The reopening of Australia's borders came as its most populous state, New South Wales, reported its biggest one-day rise in cases in four months, though Prime Minister Scott Morrison said the government was well placed to deal with rising numbers.

"We're going to live with this virus, and we're not going to let it drag us back to where we've been," Morrison told radio station 4BC. "We've got one of the highest vaccination rates, which means we can fight this thing. We don't have to surrender to it."

Australia has inoculated nearly 90% of people over the age of 16 with two doses and cut the waiting time for booster shots after the emergence of Omicron cases.

Morrison, who had been deemed a casual contact after attending an event last week along with a Covid-infected person, said he had been cleared to fly to Queensland after negative test results.

Australia closed its borders in March 2020 in a bid to contain the spread of the new coronavirus and had limited the number of citizens and permanent residents allowed to come back.

The relaxation of border rules is expected to ease labour shortages, which threaten to hamper an economic rebound.

The return of foreign students, who are worth about A$35 billion ($25 billion) a year to the Australian economy, will help businesses to fill many casual jobs. More than 235,000 foreigners, including about 160,000 students, held visas for Australia at the end of October, official data showed.

New South Wales, home to Australia's biggest city of Sydney, lifted most restrictions from Wednesday for the unvaccinated, despite a steady rise in Omicron infections after a staggered reopening.

The state logged 1,360 new cases, the biggest daily rise in more than three months and since a nearly four-month lockdown ended in early October. Australia has recorded about 235,500 cases and 2,117 deaths since the pandemic began.

New South Wales Minister for Health Brad Hazzard warned infections could rise to 25,000 a day by the end of January.

While New South Wales said its health system was coping well with the rising cases, Western Australia state said on Wednesday it would restrict the entry of people from New South Wales.