"Many variants are coming, and Omicron was the first one that was able to evade -- in a skillful way -- the immune protection that we're giving," Bourla told CBS' "Face the Nation."
"The protection we are getting from the third (dose) it is good enough -- actually quite good for hospitalizations and deaths," Bourla said.
But protection after three doses is "not that good against infections" and "doesn't last very long" when faced with a variant like Omicron.
"It is necessary, a fourth (dose) for right now," Bourla told CBS.
Currently, anyone ages 12 and up who got a second dose of the Pfizer vaccine at least five months ago can get a third dose.
Anyone ages 18 and up who got the two-dose Moderna vaccine should get a booster shot six months after the second dose, according to the US Centers for Disease Control and Prevention.
And anyone who got the single-dose Johnson & Johnson vaccine should get a booster shot after two months, the CDC said.
Some moderately or severely immunocompromised people who have had three doses of the Pfizer/BioNTech or Moderna Covid-19 vaccines can already get a fourth dose of vaccine, according to the CDC.
But it's not clear if or when the US Food and Drug Administration might authorize a fourth dose of Covid-19 vaccine for healthy teens and adults.
"We are just submitting those data to the FDA, and then we'll see what the experts also would say outside Pfizer," Bourla told CBS.
Kids under 5 might soon be able to get vaccinated
Currently, children ages 5 to 11 are eligible for two pediatric doses of Pfizer's Covid-19 vaccine but are not yet eligible for a booster. Pfizer is testing a third dose in that age group now.
And kids under age 5 are not yet eligible for a Covid-19 vaccine -- though that could change this spring, Bourla said.
Initial trial data in children ages 2 to 5 showed two doses of a smaller, child-sized vaccine didn't give the expected immunity in the 2- to 5-year-olds -- though it did for babies ages 6 months to 2 years.
So Pfizer decided to add a third child-sized dose for children under age 5 in its ongoing trial.
Pfizer should have data on its three-dose vaccine trial for children ages 6 months to 5 years by April, Bourla told CBS on Sunday.
If authorized by the FDA and recommended by the CDC, Covid-19 vaccines for children ages 6 months to 5 years might start as early as May, Bourla said.
A shot at a longer-lasting vaccine against all variants
Pfizer and Moderna have said they are working on a vaccine that would specifically protect against the Omicron variant. It's not clear yet if one is needed.
Bourla said Pfizer is also hoping to make a vaccine that will protect against Omicron and all other variants of SARS-CoV-2 -- the virus that causes Covid-19.
The goal is to create "something that can protect for at least a year," Bourla told CBS on Sunday.
"And if we are able to achieve that, then I think it is very easy to follow and remember so that we can go back to really the way (we) used to live," he said.
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