Testing capacity for the coronavirus in the U.S. will dramatically increase in the coming days, former Food and Drug Administration Commissioner Scott Gottlieb told CNBC on Friday.

"By probably next week, we'll be at capacity of tens of thousands of tests a day," Gottlieb said on "Squawk Box." "Certainly by the end of next week, I think you're going to see capacity really sharply ramp up in our ability to test patients."

Gottlieb said he believes capacity will increase because the FDA will continue to approve new tests, such as one from Swiss diagnostics maker Roche. It is an automated system, allowing for more tests to be conducted, he said.

The Roche test, given emergency approval Friday by the FDA, can give results in 3.5 hours and produce up to 4,128 results in a day, according to Reuters.

"I think you're going to see a rapid succession of approvals of these systems," said Gottlieb, a CNBC contributor who sits on the boards of Pfizer and biotech company Illumina.

Gottlieb noted that more tests running in the U.S. will produce an increased number of confirmed cases.

As of 7:25 a.m. Friday, the U.S. had around 1,700 confirmed cases and 40 deaths, according to data from Johns Hopkins University.

Gottlieb's comments come one day after a top U.S. health official admitted the country's coronavirus testing system was "failing."

"The system is not really geared to what we need right now, what you are asking for. That is a failing," said Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases.

"The idea of anybody getting it easily the way people in other countries are doing it, we're not set up for that. Do I think we should be? Yes. But we're not," Fauci testified in front of the House Oversight and Reform Committee.

Gottlieb also said Friday that Americans who are able to avoid hospitals for issues unrelated to the coronavirus should do so.

"I would try to avoid interactions with the health-care system if I can right now," he said. "I think hospitals should also be looking at canceling elected procedures to try to preserve volumes in the hospitals."

In addition to preserving the health system's capacity, it also reduces one's likelihood of contracting the virus inside a hospital, he said.

"This spreads when it gets inside institutions and inside the health-care system. That's how a lot of the virus is propagated in our countries," he said. while adding that U.S. hospitals already do strong infection control and have likely added to that regime due to the coronavirus.

"We're going to have less of those kind of problems, but there is a risk in an institutionalized setting of spreading this virus," he said.