"The problem is right now we have other vaccines like Novavax and others coming on, probably," Biden said in response to a question about aid to India amid an outbreak of the virus there. "And I think we will be in a position to share vaccines as well as knowhow in countries who have a real need."
Novavax shares closed regular Tuesday trading up 16% to $257.67.
On Monday, the White House said it would be sending its supply of AstraZeneca vaccine to foreign countries to combat the pandemic globally.
The U.S. has an inventory of 60 million doses of the AstraZeneca vaccine.
"Given AstraZeneca is not authorized for use in the United States, we do not need to use AstraZeneca in our fight against COVID over the next few months," White House Press Secretary Jen Psaki said.
Earlier this month, the EU's European Medicines Agency said the U.K.-based company's COVID vaccine was probably causing deadly blood clots in a small number of vaccinated people.
On Tuesday, the president was commenting on new Centers for Disease Control and Prevention guidelines, saying that vaccinated people can gather outdoors without a mask.
Biden targeted July 4 as the date "to get life in America closer to normal."
The CDC says that vaccinated people no longer need to wear a mask at small outdoor gatherings.
The agency still recommends masks at large outdoor gatherings like concerts and sporting events, even for people who are fully vaccinated.