• The Trump administration declined Pfizer's offer to provide the U.S. government with additional coronavirus vaccine doses in the second quarter of 2021, board member Dr. Scott Gottlieb said.
• Pfizer made an offer "multiple times" to provide more than the 100 million doses it already agreed to supply, Gottlieb told CNBC.
• The remarks confirm a report Monday from The New York Times.

Dr. Scott Gottlieb, a member of Pfizer's board, told CNBC on Tuesday the company's offers to provide the U.S. with additional doses of its coronavirus vaccine in 2021 were declined by the Trump administration.

The government in July agreed to a deal with Pfizer and its German partner BioNTech for 100 million doses of their Covid-19 vaccine if it proved safe and effective. The Food and Drug Administration is set to meet Thursday to review the companies' emergency use application. Gottlieb spoke before the agency Tuesday released the companies' clinical trial data, which revealed no specific safety concerns.

If it is approved, Pfizer's entire supply of vaccine produced in its Michigan manufacturing facility in December and the first quarter of 2021 will go to the U.S, Gottlieb said on "Squawk Box." Under that July agreement, the government could acquire an another 500 million doses.

"Pfizer did offer up an additional allotment coming out of that plant, basically the second-quarter allotment, to the United States government multiple times and as recently as after the interim data came out and we knew this vaccine looked to be effective," said Gottlieb, who previously led the FDA in the Trump administration from 2017 to 2019.

Gottlieb, whose comments confirm a report Monday by The New York Times, said he believes the U.S. government likely turned down Pfizer's offer because it wanted to make sure it diversified the number of companies it agreed to purchase option agreements with.

For example, it has an agreement in place for 100 million doses of Moderna's Covid-19 vaccine. The Massachusetts-based biotech company developed the only other vaccine currently awaiting FDA clearance. Johnson & Johnson also struck a deal with the Trump administration for 100 million doses of its coronavirus vaccine in August.

"I think they're betting that more than one vaccine is going to get authorized and there will be more vaccines on the market," Gottlieb said. "And that, perhaps, could be why they didn't take up that additional 100 million option agreement, which wouldn't really have required them necessarily to front money. It was just an agreement that they would purchase those vaccines. So Pfizer has gone ahead and entered into some agreements with other countries to sell them some of that vaccine in the second quarter of 2021."

CNBC reached out to the Department of Health and Human Services for comment on Gottlieb's remarks. In a statement later posted to Twitter, an HHS spokesperson said the department remained "confident that across our portfolio of multiple vaccines we will have enough doses for any American who wants a vaccine by the end of Q2 2021."

"We have been, and continue to, negotiate with Pfizer for additional doses," the statement also said. However, the HHS spokesperson said that the Trump administration's vaccine development program, Operation Warp Speed, never rejected "an offer from Pfizer for any number of millions of doses having a firm delivery date and quantity."

On Tuesday, people in the United Kingdom became the first to receive the Pfizer-BioNTech vaccine outside of a clinical trial after British regulators granted clearance last week. The U.K. government has ordered 40 million doses of the vaccine, which is enough for 20 million people since it requires two shots.

President Donald Trump on Tuesday signed an executive order that attempts to give Americans priority for Covid-19 vaccines that his administration helped bring to market. The government has provided billions of dollars to drugmakers to aid in vaccine development and production.

"I don't know what the legal authorities are. I suspect that there are authorities that the administration could invoke that would break some agreements that Pfizer or other companies might've struck with other countries," Gottlieb said before the signing.

"But bear in mind, the countries that the vaccine was sold to are our close allies. There is supply from that [Michigan] plant that's going to come into the United States in the second quarter. It's just not all of the supply," he added. "Some of it was promised to other countries after it was offered multiple times to the United States."

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. Gottlieb also serves as co-chair of Norwegian Cruise Line Holdings′ and Royal Caribbean's "Healthy Sail Panel."