Dr. Scott Gottlieb expects Covid vaccine appointments to be widely available by April in the U.S.

Dr. Scott Gottlieb told CNBC on Monday he expects Covid vaccine eligibility in the U.S. to be expanded significantly by April, suggesting the move will be necessary due to a lack of Americans wanting to receive the shots.

“I think we’re going to run out of demand sooner than we think. I suspect that in some point in March and certainly by the end of March, we’re going to have to make this generally available,” Gottlieb said on “Squawk Box.” “That doesn’t mean everyone can go and get a vaccine on April 1, but I think everyone is going to be able to go online and get an appointment sooner than we think.”

Demand has typically outpaced supply of available doses since the U.S. Food and Drug Administration issued emergency use authorization for Pfizer and Moderna‘s Covid two-dose vaccines in December. As such, priority was initially given to higher-risk individuals, such as frontline health care workers and nursing home residents. It’s now been expanded across states to include people who are 65 years old and up, as well as professions such as teachers and law enforcement.

The Biden administration also is expected to begin sending vaccine doses directly to retail pharmacies across the U.S. in the coming days.

Gottlieb, a former FDA commissioner from 2017 to 2019 in the Trump administration, said he believes supply constraints will remain throughout February that justify having more narrow eligibility criteria. “But at some point in March, states are going to have to make decisions about how to open this up more widely,” predicted Gottlieb, who serves on Pfizer’s board of directors.

“If we continue to ration it based on more and more narrow slices of the population, it’s going to get harder to administer, so I think we’re just going to have to open this up to general availability, which is good news,” he added.

The vaccine rollout in the U.S. started slower than expectations, but the pace has improved in recent weeks. As of Sunday morning, there have been 41.2 million total doses administered, according to data compiled by the Centers for Disease Control and Prevention. Just over 9.1 million people have received both shots of the two-dose vaccines, CDC data shows.

A third Covid vaccine maker has applied for emergency use authorization with the FDA. Johnson & Johnson’s application is set to be discussed by an FDA advisory panel Feb. 26. The company’s vaccine has been widely anticipated because it requires only a single dose, and Gottlieb has previously said it would be a “great addition” to the market.

But even with more supply available in the coming months, Gottlieb stressed the need for a concerted effort to make U.S. residents trust the lifesaving vaccine.

“We’re going to have to work on it to try to get the incremental patients vaccinated. I think demand here … is deep but not wide,” he said. “There’s probably about, maybe, 100 million Americans that want this very badly. Beyond that, we’re going to have to work on it.”

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