The US coronavirus testing system needs a major overhaul for faster results, said Dr. Scott Gottlieb told CNBC on Tuesday: He also warned Americans not to expect quick fixes.

“The system that we currently have – as discontinuous as it is and problematic as it is – has been built really organically, and that’s part of the problem,” the former Commissioner of the Food and Drug Administration told Squawk Box. “You don’t have an efficiently operated system because nobody really built it rationally.”

Even so, Gottlieb said the U.S. has reached a point over the nearly year-long pandemic where it can do “an enormous amount of testing.” He found that more than 2 million new tests are done in a few days. According to a CNBC analysis of data compiled by the COVID Tracking Project, the country’s seven-day average is nearly 1.8 million new tests per day.

“I think it’s the way the system is organized right now that the samples aren’t getting into laboratories that have the capacity fast enough for people to get a timely result back,” he said. “There are many PCR-based test platforms, but in many cases the samples do not get to where the capacity is available. Therefore this is currently an organizational challenge.”

Polymerase chain reaction, or PCR, tests are the most accurate type of Covid test and involve sending a nasal or saliva sample to a laboratory for processing. Rapid antigen tests can play an important role, Gottlieb said, especially for people who have Covid symptoms. But even someone who tests positive through a quick screening may need a PCR test to confirm their infection, he said.

In the near future, Gottlieb anticipates that the processing time for Covid test results will improve as demand diagnostic tests will decrease. “The infection rates are falling,” said Gottlieb, who headed the FDA in the Trump administration from 2017 to 2019.

The US is seeing 146,019 new coronavirus cases per day, based on a seven-day average. This comes from a CNBC analysis of the data compiled by Johns Hopkins University. That’s less than the seven-day average of 176,114 on Jan. 23.

“People, when they are less likely to have an infection, less likely to be symptomatic, are less likely to get a test,” said Gottlieb. This is a positive development, he said, because it will take some time for the US test system to be more coherent and for the organizational challenges to be smoothed out. He said he didn’t expect much improvement until summer, which suggests that fall is a more realistic destination.

Even though millions of Americans have been vaccinated against Covid-19, tests still need to be done, Gottlieb said. “We have to expand this for the fall, when the test volumes rise again and we are put under pressure again,” said Gottlieb, who is on the board of directors at Pfizer, which produces a Covid vaccine.

“We have to be able to do three, four million tests a day and get a result back in 24 hours or else … it’s useless,” he added. “A PCR-based result that takes longer than a day or two doesn’t make sense.”

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