The Omicron variant has now been reported in at least 23 countries around the world, the World Health Organization (WHO) said.
It comes as the group said they expected experts to have more information on the transmissibility of the variant, first identified in South Africa, "in a few days."
So far at least 32 cases of Omicron have been identified in the UK, with a number expected to rise further.
Earlier this week, Boris Johnson announced that to deal with the new Omicron variant, all people in England eligible for a coronavirus booster will be offered one by the end of January.
The government has now secured a deal for another 114 million injections for "future proofing" the UK's Covid vaccination program.
How do I book a Covid booster shot and when can I get it?
But at Wednesday's press conference, the WHO suggested that the main goal of all governments should be to ensure that all vulnerable people have been offered at least their first dose of vaccine.
"It is difficult for some countries that have large quantities of excess vaccine to decide who to administer, but that is not the problem faced by many countries around the world that cannot even receive primary vaccination for the most vulnerable." Said Dr. Michael Ryan in response to a question about England's booster program.
"It is a luxurious position to be in if you are in a position to be able to have enough vaccines to do that."
Dr. Ryan added that he was not aware of any evidence to suggest that offering Covid booster vaccines to entire populations "will provide greater protection to otherwise healthy people against hospitalization or death."
"The real risk of serious illness, hospitalization and death lies in particularly vulnerable and at risk people who require protection against all variants of Covid-19," he added.
WHO urges governments around the world to vaccinate vulnerable people first
Amid some concerns that the Omicron variant could evade available vaccines, WHO's Dr. Maria Van Kerkhove highlighted in Wednesday's briefing: "There is no indication that the vaccine is not working."
She added that even with a possible reduction in efficacy, "it is still better to have the vaccine."
In fact, European Commission President Ursula von der Leyen said on Wednesday that EU nations should consider making vaccines mandatory because too many people still refuse to voluntarily receive injections.
The vaccination rate in the EU is 66%, and unexpected spikes in cases across much of the 27-nation bloc have prompted many member countries to renew mask requirements and take other steps to curb infections.
Ms Von der Leyen said it was "understandable and appropriate" to have a discussion on "how we can encourage and potentially think about mandatory vaccination within the European Union."
How far has the Omicron variant spread, and what are countries doing to stop it?
In the UK, those who have tested positive for the variant are isolating themselves, as are their contacts, while working to establish whether there is any link to travel to southern Africa.
The UKHSA said it has now identified Omicron cases in the East Midlands, East of England, London, South East and North West, bringing England's total to at least 22.
One more case has also been identified in Scotland, the agency said, bringing the national total to at least 10.
It comes as the latest Covid data shows another 48,374 lab-confirmed Covid-19 cases in the UK at 9am. Wednesday. While 171 more deaths have been reported within 28 days of testing positive.