"We know we are now in a race against time," said European Commission chief Ursula von der Leyen. Vaccine manufacturers needed two to three weeks "to get a full picture of the quality of the mutations", she added.
A long list of countries has already imposed travel restrictions on southern Africa, including key travel hub Qatar, as well as the United States, Britain, Indonesia, Saudi Arabia, Kuwait and the Netherlands.
Angola became the first southern African country to suspend all flights from its regional neighbours Mozambique, Namibia and South Africa.
South Africa's president Cyril Ramaphosa on Sunday called on countries to lift the travel bans "before any further damage is done to our economies".
Malawi's president Lazarus Chakwera accused Western countries of "Afrophobia" for shutting their borders.
The head of the World Health Organization in Africa also urged countries to follow the science rather than impose flight bans in a bid to contain the new Covid strain.
"With the Omicron variant now detected in several regions of the world, putting in place travel bans that target Africa attacks global solidarity," said WHO regional director Matshidiso Moeti.
Race to determine threat level
Dutch health authorities said they had identified at least 13 cases of Omicron among 61 quarantined passengers who tested positive for coronavirus after arriving from South Africa.
Border police there announced Sunday they had arrested a couple on a plane at Schiphol Airport after they fled a hotel where the passengers were being quarantined.
Despite the new threat, tens of thousands rallied in Austria to protest the government's introduction of compulsory vaccination -- the first EU country to do so.
Chancellor Alexander Schallenberg said it was "a minor interference" compared to the alternative for a country with one of the lowest vaccination rates in Western Europe.
With many European nations, including Germany and France, already re-introducing restrictions to counter surges in infections, Swiss voters firmly backed a proposed Covid pass law in a referendum Sunday.
In Britain, health secretary Sajid Javid said new Covid rules will be enforced from Tuesday, including mandatory mask-wearing in shops and on public transport in England, and tighter restrictions on passengers arriving from abroad.
As scientists try to determine the level of threat posed by the new strain, one South African doctor said dozens of her patients suspected of having the Omicron variant had only shown mild symptoms, such as fatigue.
Angelique Coetzee, chair of the South African Medical Association, told AFP she had seen 30 patients over the past 10 days who tested positive for Covid-19 and who all fully recovered without hospitalisation.
Senior US government scientist Anthony Fauci said he "continues to believe that existing vaccines are likely to provide a degree of protection against severe cases of Covid", during a briefing on the new variant with president Joe Biden on Sunday.
Israel raises 'red flag'
Israel announced some of the strictest curbs, closing the borders to all foreigners -- just four weeks after re-opening to tourists following a prolonged Covid-driven closure.
"We are raising a red flag," Israeli prime minister Naftali Bennett said.
But the new strain has already slipped through the net and has now been found everywhere from the Netherlands to the UK, Botswana, Hong Kong and Australia.
Canada became the latest country to announce its first detected cases Sunday in two people who had travelled to Nigeria.
Scientists in South Africa said they had last week detected the new variant with a far greater number of mutations than in the cases of earlier strains like Beta or Delta -- the latter of which dented the global recovery and sent millions worldwide back into lockdown.
The prestigious Bambino Gesu hospital in Rome produced the first "image" of the new strain and confirmed there were many more mutations than seen in the Delta variant. But that does not mean it is more dangerous, the researchers said.