The Trump administration did not adequately respond to the threat posed by the coronavirus, Northwell Health CEO Michael Dowling told CNBC on Tuesday.

"I do think that the federal government was slow to respond," Dowling said on "Squawk on the Street." "We activated our emergency management system six weeks ago when at the federal level people were talking about, 'Don't worry about this; it's going to go away.'"

Dowling did not reference comments from a specific government official, but National Economic Council Director Larry Kudlow said on Feb. 25, "We have contained this. I won't say [it's] airtight, but it's pretty close to airtight." At that point, there were less than 60 confirmed cases in the U.S. There are more than 760 now, according to data from Johns Hopkins University.

White House spokesman Judd Deere pushed back on the suggestion that President Donald Trump was slow to respond to the coronavirus. "Very early he took decisive actions like instituting travel restrictions and utilizing quarantine authority and he is prepared to take additional action," Deere wrote in an email.

Northwell Health is the largest health-care provider in New York, operating 23 hospitals and nearly 800 outpatient facilities across the state. New York has 148 confirmed cases of the coronavirus, the second most in the U.S. behind Washington state.

"This is actually going to get worse before it gets better. We don't know how long it's going to take," Dowling said. "But we, in our health system, along with working with all the other health systems, we're pretty well prepared."

Northwell received federal approval Sunday to conduct manual coronavirus tests at its laboratory on Long Island.

Dowling said it took too long for Northwell to receive approval, saying the nonprofit hospital system "had been urging to move the process along more quickly for many, many, many weeks."

New York Gov. Andrew Cuomo has been critical of the federal government for not allowing more local facilities to do tests.

"It's one thing for the federal government not to have the testing capacity in place themselves — that was bad enough — but there's no excuse for them not to be authorizing existing labs to do the work," Cuomo said Sunday, according to The Journal News.

On Tuesday afternoon, Cuomo said he plans to deploy the National Guard to New Rochelle, a coronavirus hot spot just north of New York City.

Meanwhile, the Centers for Disease Control and Prevention have taken steps during the course of the outbreak to make it easier for more facilities to conduct tests. It also eased restrictions on who could be tested.

The CDC, in an email response to CNBC, said the agency "established a COVID-19 Incident Management System on January 7," and two weeks later "activated its Emergency Operations Center to better provide ongoing support to the COVID-19 response."

Northwell is now hoping to receive approval from the U.S. Food and Drug Administration to conduct automated tests for the coronavirus, Dowling said. It can manually process around 75 to 80 tests per day.

If automated testing were approved, Dowling said Northwell could quickly begin to conduct 1,000 tests per day and "probably up to 2,000 tests a day when it's fully operational, because we've got to ramp this up."

However, Dowling stressed that testing everyone would be a mistake. He said health officials must prioritize those who are showing symptoms and those who have been in contact with someone who has the disease.

Doing so would help minimize the public's fear toward the outbreak, Dowling said. "We've got to keep people calm. Keep people realistic. Focus on the issue and solve it," he added. "We will win this. You can defeat this like we've done with Ebola, SARS, H1N1."