Dr. Scott Gottlieb said Monday he saw promising signs that Covid vaccines, in addition to their well-documented ability to protect against serious illness, are effective in reducing the spread of the virus from person to person.

In an interview on CNBC’s “Squawk Box,” the former Food and Drug Administration commissioner warned that while the early data looks positive, there are still some uncertainties. “I think there is a reduction in transmission. The question is, how big is that?” said Gottlieb, a member of the Pfizer board of directors.

The company’s vaccine, developed jointly with German drug maker BioNTech, is one of three vaccines that have received FDA approval for emergencies. The other two are made by Moderna and most recently Johnson & Johnson, which received limited approval from U.S. regulators on Saturday.

The FDA granted emergency approval to the trio of vaccines after individually determining that they were safe and effective in preventing recipients from developing symptomatic Covid disease, particularly severe cases and deaths. What has been less clear since the US began administering vaccines against Pfizer-BioNTech and Moderna in December is specific data aimed at limiting the spread of the virus. This is one of the reasons doctors have urged even those who have been vaccinated to continue to take precautions.

For example, in its press release announcing that the vaccine had received emergency approval from J&J, the FDA stated that there was no “evidence that the vaccine could transmit SARS-CoV-2 represents person to person “.

However, Gottlieb said there was reason to be optimistic that the vaccines would do just that, even though “the final study” proves it has not yet done so. “The evidence gathered is very convincing that transmission will be reduced,” said Gottlieb, who headed the FDA in the Trump administration from 2017 to 2019.

He pointed to two studies done in Israel, one of the world’s leading countries for vaccinating its population, that suggest the Pfizer BioNTech vaccine reduces virus transmission. Gottlieb also said that J&J in his study found a 74% reduction in participants who developed asymptomatic infection. This finding from J&J, Gottlieb said, “is a pretty good indication that transmission is reduced.”

“I think most people will agree … people who are vaccinated are less likely to transmit the infection if they infect themselves,” said Gottlieb, adding he expects a more definitive answer “within the next one or two two months”.

J&J Chairman and CEO Alex Gorsky said Monday on Squawk Box that the company’s initial findings on preventing asymptomatic infection were encouraging and signaled the possibility of “heavily denting” the Covid pandemic. “But we need to collect more. We would expect to literally collect that in the coming months if we continue to track these patients in the study,” he said.

Disclosure: Scott Gottlieb is a CNBC employee and a member of the boards of directors of Pfizer, genetic testing startup Tempus, healthcare technology company Aetion, and Illumina biotech. He is also co-chair of the Healthy Sail Panel for Norwegian Cruise Line Holdings and Royal Caribbean.