The first batch of government-authorized coronavirus tests from Thermo Fisher Scientific have shipped off and the "dramatic ramp up" in production has begun, CEO Marc Casper told CNBC Monday.

"We have already about 1.5 million tests in stock. We began shipping them yesterday and today," Casper said in a "Mad Money" interview with Jim Cramer. "But we're ramping up to about 2 million tests in production a week, and then over the course of April we'll be able to get that to about 5 million tests a week in terms of production."

Thermo Fisher is one of two diagnostics makers to receive emergency use authorization (EUA) from the U.S. Food and Drug Administration for coronavirus tests that are badly needed in the rush to slow the spread of the deadly COVID-19, the disease caused by the novel virus that has infected and killed thousands across the globe. Swiss diagnostics maker Roche is the other company granted authorization for a similar device.

Thermo Fisher's coronavirus test, an instrument called Applied Biosystems 7500 Fast Dx Real-time PCR, has not been FDA approved, though the EUA permits its use to diagnose the novel virus in patients. The EUA can be issued when the U.S. Department of Health and Human Services declares a public emergency. HHS Secretary Alex Azar made that declaration Jan. 31.

The test has been shipped to 200 laboratories across the country and can be administered at a doctor's office or a testing center, Casper said.

"Those samples will then be brought to a laboratory and each state will know which laboratories have the tests," he explained, "and then once the process starts, it's about four hours from the receipt of the test at a laboratory to actually getting a result."

The update comes as the Trump administration races to meet testing demands and financial markets crumble under uncertainty. Trump has blamed his administration's lag in testing for the virus on rules and regulations inherited from the previous administration.

In a news conference held in the White House Rose Garden earlier on Friday, Trump said the federal government was partnering with the private sector to ramp up test kit production to make them more widely available to Americans.

There are at least 168,019 cases and 6,610 deaths recorded around the world due to COVID-19, according to the latest data from the World Health Organization. In the U.S., more than 4,600 have contracted the virus and 85 have died as of Monday, according to Johns Hopkins University's latest figures.

New York, Washington and California have recorded the largest outbreaks across the country. The virus has spread to all but one state, according to the university.

When asked about the quality of Thermo Fisher's test to Roche's, Casper struck a unified tone.

"There's only one competitor out there, and that's the virus," he said. "Expanding that [testing] capacity so that it's across the country and in other countries as well is super important in addressing the virus."

Shares of Thermo Fisher slid nearly 7% to $279.32 a piece after Monday's steep market sell-off.