Two of the largest private labs in the U.S. will collectively be able to process more than 300,000 COVID-19 tests by the end of the week, their CEOs say.

LabCorp CEO Adam Schechter told CNBC's "Squawk Box" on Tuesday the company is processing around 20,000 tests daily and will by the end of the week be able to "a lot more" than 100,000 tests per week.

Quest Diagnostics is conducting about 25,000 COVID-19 tests per day, with plans of increasing daily capacity to around 30,000 by the end of the week, CEO Steve Rusckowski told CNBC's "Closing Bell" a day earlier.

That would put Quest's weekly capacity around 200,000, he said.

"By the end of this week we're going to have significantly more testing capacity in this country than we had only a week or so ago," Rusckowski said.

Said Schechter: "Next week will be significantly more than this week."

Quest began processing its test on March 9 while LabCorp's test became available a few days earlier.

While testing capacity in the U.S. has lagged behind other nations, Schechter stressed the importance now of considering all the different entities who are conducting tests.

"It's not just about LabCorp," he said. "When you think about the other national, regional, local labs, academic medical centers, hospitals and the state labs, everybody is increasing capacity."

Increasing testing capacity is critical in understanding just how widespread COVID-19 is in the U.S.

"It's impossible to know the exact number that we'll need, but I know we'll build as much capacity as we can," Schechter said.

As of Tuesday morning, there are more than 46,000 confirmed cases in the U.S., including nearly 600 deaths, according to Johns Hopkins University data.