The World Health Organisation has branded herd immunity a "dangerous" concept and warned trying to achieve it puts lives at risk.
The WHO said "no-one is safe until everyone is safe" - and said it is "dangerous" to think that countries can "magically reach herd immunity".
Although the UK government has denied adopting this approach in the early days of the pandemic, many experts believe this was the initial goal.
Sweden has refused to introduce a full lockdown, and scientists there are optimistic that a large proportion of the population will develop antibodies.
The term 'herd immunity' describes how a population is protected from a disease if enough people develop immunity through antibodies created by the illness or a vaccination.
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Dr Mike Ryan, executive director of the WHO's health emergencies programme, told a press briefing in Geneva that it is not a feasible policy.
He said: "Humans are not herds, and, as such, the concept of herd immunity is generally reserved for calculating how many people will need to be vaccinated and the population in order to generate that effect.
"This is a serious disease, this is public enemy number one, we have been saying it over and over and over and over again."
He said "no one is safe until everyone is safe", adding: "So I do think this idea that 'maybe countries who had lax measures and haven't done anything will all of a sudden magically reach some herd immunity, and so what if we lose a few old people along the way?' - this is a really dangerous, dangerous calculation."
Dr Ryan continued: "Responsible member states will look at all their population - they value every member of society and they try to do everything possible to protect health while at the same time, obviously, protecting society and protecting the economy and other things.
"We need to get our priorities right as we enter the next phase of this fight."
Dr Maria Van Kerkhove, technical lead of the WHO's Covid-19 response, said preliminary data from studies has shown that very low levels of the population have actually been infected with the illness.
"There seems to be a consistent pattern so far, that a low proportion of people have these antibodies," she said.
"And that is important, as you mentioned, because you mentioned this word 'herd immunity', which is normally a phrase that's used when you think about vaccination.
"You think what amount of the population needs to have an immunity to be able to protect the rest of the population?
"We don't know exactly what that level needs to be for Covid-19.
"But it certainly needs to be higher than what we're seeing in seroprevalence studies.
"What the sero-epidemiologic studies indicate to us is that there's a large portion of the population that remains susceptible."
