"We need all states to ensure we're doing everything we can to better control the virus. If we can do that, then we'll be able to have the tests that we need," Schechter said on "Closing Bell."
LabCorp is currently processing about 165,000 tests for Covid-19 per day, translating to more than 1 million per week, he said. In late March during the early stages of the pandemic, LabCorp was running about 20,000 tests per day.
"We're continuing to increase capacity every single week over week," he said. "The problem is that the number of tests being asked to be performed each week is growing faster than the capacity that we can build."
For someone in the hospital, LabCorp is able to return Covid-19 tests results within 1.5 days on average, Schechter said. Average turnaround time is about three to five days for someone who isn't in the hospital, he said, while a range of about two to three days is needed to have an "effective ability to track and trace people that are sick or have been exposed to people."
Like LabCorp, Quest Diagnostics also has warned that its turnaround time for testing results has slowed as transmission of the virus spreads in certain parts of the U.S., especially across the American South, Southwest and West.
In the last 7 days, the U.S. has averaged nearly 763,000 diagnostic tests per day, according to a CNBC analysis of data from the Covid Tracking Project. The national average in April was about 174,000 diagnostic tests per day, per a CNBC analysis.
The overall rise in new Covid-19 cases in the U.S. can only be partly attributed to added testing capacity. That's because the test positivity rate also has increased, an indication of how broadly the virus is spreading throughout a community.
The U.S. has an 8.5% positivity rate, based on a seven-day moving average, according to Johns Hopkins University. In early June, the seven-day moving average had dropped below 5% nationally. At times in April, the U.S. positivity rate was around 20%.
Schechter said he believes the U.S. needs to be "really thoughtful" about demand for Covid-19 testing as it approaches the fall — a time when students may be heading back to school and more people potentially ease out of working from home.
"I am concerned about it, but we have to look at it holistically," he said, stressing the need for American residents to wear face masks and continue practicing social distancing. He added that quicker turnaround time for tests is a part of the solution, along with further progress on research for vaccines and therapeutics.
"If we pull those things together, I believe we can beat this virus and get the country up and running again in a very significant way," he said.