Dr. Scott Gottlieb on Thursday warned coronavirus vaccine recipients against letting their guards down right away, telling CNBC they should adhere to public-health measures such as wearing masks.

The former U.S. Food and Drug Administration commissioner said the advice is particularly important for elderly Americans who are at higher risk of death or serious illness from Covid-19.

“I think for an older individual who is vulnerable to this virus, certainly .. wait for a period of time after the second shot until you’re likely to have full protective immunity,” Gottlieb said on “Squawk Box.” “I don’t think people should feel completely secure after the first shot.”

Both Covid vaccines that have received emergency use authorization from the FDA require two doses. Pfizer and its German partner BioNTech developed one of the vaccines, while Moderna makes the other. Gottlieb sits on the board of Pfizer.

Roughly 10.3 million Americans have received their initial Covid shot, as of Wednesday morning, according to the Centers for Disease Control and Prevention. About 29.4 million doses have been distributed.

The shaky vaccine rollout comes as the nation continues to see high levels of coronavirus infection and more deaths from Covid-19. The country’s seven-day average of new daily cases is 245,306, according to a CNBC analysis of data compiled by Johns Hopkins University. An average of 3,360 Americans have died from Covid per day over the last week, the second-highest tally on record.

Vaccine recipients need to still take public-health precautions because the U.S. outbreak remains so significant and “infection is everywhere,” Gottlieb said. “If you’re a vulnerable individual, even if you’ve had the second shot and you think you have full protective immunity from the vaccine, it’s still very prudent to continue to wear a mask and take precautions.”

“That doesn’t mean you have to hibernate and have to avoid seeing family,” added Gottlieb, who led the FDA in the Trump administration from 2017 to 2019. “Maybe you can lean forward in that regard but wear a mask. Be more careful in those interactions, because in a high-prevalent environment, you’re still at risk.”

As more Americans become vaccinated, Gottlieb said that should lower overall U.S. infection rates and significantly curtail the intensity of the epidemic. At that point, he said, it will be more sensible to “relax” some precautions.

“That’s hopefully going to be the summer, the spring, if these new variants don’t get a foothold here in the United States and change our trajectory,” he said, referencing the coronavirus strains initially found in the U.K. and South Africa that are believed to be more transmissible.

Researchers in Ohio said Wednesday they’ve discovered two new variants that likely originated in the U.S. 

Last week, Gottlieb cautioned Americans that returning to pre-pandemic life is unlikely to happen in 2021. For example, he told CNBC that public venues may still be requiring people to have their temperature taken before entry.

“I just think things are going to be different, just like they’re different when you go through an airport now after 9/11,” he said last week. “I don’t think masks are going to be mandatory next fall and winter if we can get the vaccination rate up and if these new variants go away or don’t become prevalent. But I do think a lot of people will want to wear masks, and that’s OK.”

Disclosure: Scott Gottlieb is a CNBC contributor and is a member of the boards of Pfizer, genetic testing start-up Tempus and biotech company Illumina. He also serves as co-chair of Norwegian Cruise Line Holdings’ and Royal Caribbean’s “Healthy Sail Panel.”