The actual number of coronavirus cases in the United States is likely significantly higher — as much 10 or even 20 times higher — than the tally of Covid-19 infections currently being reported, a former top federal health official said Tuesday.

"There's certainly under-diagnosis going on," Dr. Scott Gottlieb said during an interview with CNBC's "Squawk Box."

As of Tuesday, there were more than 787,900 coronavirus cases officially diagnosed in the U.S., with at least 42,364 deaths from the virus.

The actual number of cases "probably is 10 times as many," said Gottlieb, a former commissioner of the U.S. Food and Drug Administration and a CNBC contributor.

"We're probably diagnosing 1 in 10 to 1 in 20 infections, and that's what some of the reliable analyses are now showing," he said.

If Gottlieb is correct, that would mean that there are between almost 8 million and 15.75 million Americans who already have contracted the coronavirus, or between 2.4% to 4.8% of the U.S. population.

But it would also mean that the death rate from coronavirus cases could be markedly lower than official reports.

Gottlieb spoke a day after the publication of an analysis of the coronavirus outbreak in Los Angeles County, which estimated that the number of actual cases there is between 28 and 55 times greater than the number of confirmed cases, which as of Monday was just under 8,000.

The University of Southern California and the Los Angeles Department of Public Health, citing antibody testing of about 863 people, estimated that slightly more than 4% of LA County's adult population has antibodies to the coronavirus.

The research estimates that there are actually 221,000 to 442,000 adults in the county who have been infected.

Gottlieb cautioned Tuesday that the LA analysis, and another study conducted in California, are claiming an ability to accurately detect antibodies that is "higher than any test on the market."

He said that "small differences in the specificity of the test have a big difference on the reliability of the test ... so I think you need to put those particular valuations in perspective."

"They might be pretty off, but most of the evaluations we have now, whether it's from Seattle, or from Europe, or the ones out of New York, suggest that anywhere from 1% to 5% of people in hot spots have been exposed to this virus," Gottlieb said.

"And so, if you apply that to New York, you know, it might be that upwards of 1 million people have been exposed to this now in New York City and in the metro New York area."

"And so that puts us at a case fatality rate of around 1%, perhaps a little less — what we've been figuring all along," he said.