The emergence of omicron has also revived worries about the economic recovery from the two-year pandemic. Battered stocks and oil prices recovered somewhat after a day of panic last week, however, as hopes grew that the variant might prove to be milder than initially feared.
The World Health Organisation advised its 194 member nations that any surge in infections could have severe consequences, but said no deaths had been linked to the new variant.
An infectious disease expert from South Africa, where scientists first identified Omicron last week, said it was too early to say whether symptoms were more severe than previous variants, but it did appear to be more transmissible.
Professor Salim Abdool Karim also said existing COVID-19 vaccines are probably effective at stopping omicron from causing severe illness. Scientists have said it could take weeks to understand the severity of omicron.
Fears the new variant might be resistant to vaccines helped wipe roughly $2 trillion off global stock markets on Friday but markets settled down again on Monday, even after Japan said it would close its borders to foreigners.
Other countries also imposed travel and other restrictions, worried that omicron could spread fast even among people with immunity from vaccination or prior infection.
Travellers stranded at Johannesburg international airport said they felt "helpless" as flights from South Africa were cancelled.
"We don't know what to do, we are just waiting here, we don't know how they will help, but they just told us they can't help us," said Ntabiseng Kabeli, a stranded passenger from Lesotho.
WHO chief Tedros Adhanom Ghebreyesus said omicron's emergence showed how "perilous and precarious" the situation was.
Portugal found 13 cases of the variant at a Lisbon football club. Scotland and Austria also reported their first cases.
Japan described its ban on arrivals by foreigners as precautionary.
"These are temporary, exceptional measures that we are taking for safety's sake, until there is clearer information about the omicron variant," Prime Minister Fumio Kishida said.
Health Minister Shigeyuki Goto said tests would determine if a traveller from Namibia was Japan's first omicron case.
In Israel, a ban on arrivals by foreigners took effect overnight.
US President Joe Biden will speak at around 1645 GMT after meeting his COVID-19 team. Health officials urged Americans to get vaccines and booster shots.
"Obviously, we're on high alert," Dr Anthony Fauci, the top US infectious disease official and Biden's chief medical adviser, told ABC News. "It's inevitable that, sooner or later, it's going to spread widely."
South African cases are likely to top 10,000 a day this week, rocketing up from barely 300 a day two weeks ago, Abdool Karim said.
But South African President Cyril Ramaphosa denounced "unjustified and unscientific" travel bans that damage tourism-reliant economies. His country has said it is being punished for its scientific ability to detect new variants.
After a virtual meeting on Monday, G7 health ministers praised South Africa for its "exemplary work" in detecting the variant and alerting others to it.
UN Secretary-General Antonio Guterres expressed concern that travel restrictions would leave southern African countries isolated.
"The people of Africa cannot be blamed for the immorally low level of vaccinations available in Africa – and they should not be penalised for identifying and sharing crucial science and health information with the world," he said.
Guterres has long warned about the dangers of vaccine inequality around the world and that low immunisation rates are "a breeding ground for variants."
With the WHO urging members to speed up vaccinations of high-priority groups, the Philippines began a drive to inoculate nine million people in three days, deploying security forces and thousands of volunteers.
"Omicron has an unprecedented number of spike mutations, some of which are concerning for their potential impact on the trajectory of the pandemic," the WHO said.
More than 261 million people in over 210 countries have been reported to be infected by the coronavirus since the first cases were identified in China in December 2019 and 5,456,515 have died, according to a Reuters tally.
European Central Bank chief Christine Lagarde meanwhile tried to reassure investors that the euro zone could cope with a resurgence of infections.
"There is an obvious concern about the economic recovery in 2022, but I believe we have learnt a lot," she told Italian broadcaster RAI late on Sunday.
"We now know our enemy and what measures to take. We are all better equipped to respond to a risk of a fifth wave or the omicron variant."