Australia will continue its path towards a Christmas reopening while health authorities gather more information about the new strain.
Chief Medical Officer Paul Kelly told the state and territory heads it would be up to two weeks before there was enough information to paint a clear picture about the variant's threat.
But he said there was no evidence that vaccines were less effective.
Mr Morrison said during Question Time on Tuesday that his government had taken "sensible precautions" in delaying this week's planned reopening of international borders for visa holders until 15 December.
About 200,000 workers and students were expected to start arriving in Australia from Wednesday, but that has now been delayed by at least two weeks.
The reopening to fully vaccinated travellers from Japan and South Korea has also been paused until 15 December.
"We have taken sensible precautions for a two-week pause for the next steps," Mr Morrison said.
"As we continue to face these new variants of concern, and it is a variant of concern, we've dealt with many before."
Mr Morrison said it was crucial state and territory leaders stick to their reopening plan.
"We're not going back to lockdowns, none of us want that," he said.
"What we did last night was protecting against that, by having a sensible pause."
Tasmania on Tuesday afternoon announced it would be closing its borders to the vast majority of overseas arrivals.
Any traveller who has spent time in any overseas location – excluding New Zealand’s south island - since 28 November will not be permitted to enter Tasmania, a post on the government’s website read.
Anyone attempting to travel to Tasmania and who has spent time overseas in the 14 days prior to 28 November will not be permitted to enter unless approved as an essential traveller.
The federal government on the weekend stopped flights from eight southern African countries, where the variant was first detected, and brought in quarantine requirements from anyone who recently entered Australia from the region.
Victoria and New South Wales on Tuesday announced additional quarantine measures for those travellers.
Prof Kelly told reporters on Tuesday morning health authorities knew the spread of the Omicron variant could not be held off indefinitely.
"We cannot keep this Omicron variant out forever from Australia - eventually it will be here," he said.
"Most importantly is now we do what we can to slow down that introduction and all of the measures that have been introduced will assist with that."
Omicron delays border reopening for visa holders
Professor Kelly said the cases of Omicron in Australia had so far shown "very mild or no disease" but the variant continued to be assessed.
"We do know it's transmissible. We don't know still about the vaccine effectiveness. We don't know about severity and there's mixed reports on that," he said.
He said health authorities were working with international partners and directly with the World Health Organization to monitor the situation "very actively".
Omicron has prompted a swathe of countries across the globe to limit travel from southern Africa.
National cabinet met on Tuesday afternoon to discuss concerns posed by the new variant, and current measures in place to reduce its spread in Australia.
With additional reporting by AAP.