• Hospitals are vaccinating fewer people than they could be due to shortages in available doses, Dr. Scott Gottlieb told CNBC on Friday.
• "I don't think that they're going to catch up next week even after the Moderna doses ship and you start having more supply in the channel," the Pfizer board member said.
• Confusion about available doses arose after vaccinations began earlier this week.

Dr. Scott Gottlieb told CNBC on Friday he expects a shortage of Covid-19 vaccine doses to continue past next week, even if the Food and Drug Administration issues emergency use authorization for Moderna's vaccine.

"I've talked to hospitals. They're vaccinating far fewer health-care providers than what they could be because they just don't have the doses available," the former FDA chief and Pfizer board member said on "Squawk Box." "I don't think that they're going to catch up next week even after the Moderna doses ship and you start having more supply in the channel."

Suresh Gunasekaran, CEO of University of Iowa Hospitals & Clinics, painted a similar account to CNBC.

"We received one Pfizer batch earlier this week with 975 doses, and we can report that we concluded vaccinating 975 people yesterday," Gunasekaran said Friday on "Squawk on the Street." "To be perfectly honest, if we needed to vaccinate double or triple that amount in the last few days, we could have. Really the availability of vaccine was really our rate limiting step."

The U.S. began administering shots to health-care workers Monday, just days after Pfizer and BioNTech's Covid-19 vaccine received limited regulatory approval. However, confusion has arisen in recent days as some governors across the country have said they now expect to receive fewer doses than anticipated in the coming weeks.

The Department of Health and Human Services has pushed back on those suggestions, telling CNBC in a statement that reports that "jurisdictions' allocations are being reduced are incorrect." The statement added, "As was done with the initial shipments of Pfizer vaccine, jurisdictions will receive vaccine at different sites over several days."

In a statement Thursday, Pfizer said its manufacturing has not experienced any disruptions despite claims from Republican Florida Gov. Ron DeSantis earlier this week that the drug company has had a production issue leading to dose shortages.

"This week, we successfully shipped all 2.9 million doses that we were asked to ship by the U.S. Government to the locations specified by them," Pfizer said. "We have millions more doses sitting in our warehouse but, as of now, we have not received any shipment instructions for additional doses."

The U.S. government has said it plans to ship 2 million doses of Pfizer's vaccine next week. Moderna's vaccine could receive emergency approval as soon as Friday, and U.S. officials have said that just under 6 million doses of its vaccine could be shipped next week.

Gottlieb told CNBC he believes some of the confusion around available supply of Pfizer's vaccine could be stemming from government concerns about the logistics network. He said there may be the desire to temper the supply of Pfizer's vaccine in the system to make sure the distribution network can handle it and doses don't pile up anywhere.

"I think they should be taking some risk and leaning forward, trying to get more doses in people's arms, both Moderna and Pfizer," Gottlieb said, noting the current intensity of the U.S. epidemic. "I think getting as much protective immunity out into the population as possible is very important right now."

Hospital workers and residents of long-term care facilities are receiving priority in the initial wave of vaccine distribution. "I think they could have pushed out more vaccine through the hospitals this month than what they're doing. We could vaccinated many more people," Gottlieb said.

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. Pfizer has a manufacturing agreement with Gilead for remdesivir. Gottlieb also serves as co-chair of Norwegian Cruise Line Holdings′ and Royal Caribbean's "Healthy Sail Panel."