Vice President Pence, speaking to Fox News' "Sunday Morning Futures," warned that "we know that there will be many more cases" of coronavirus in the United States and that President Trump had ordered the stockpile of masks to increase from 43 million to approximately "that amount on a monthly basis."

Pence also announced that the Trump administration has "expedited" the process to produce a coronavirus vaccine, and that clinical trials will begin within an "utterly unprecedented" six weeks. Although the vaccine likely won't be available "this season," Pence said, work was proceeding as quickly as possible under the circumstances.

At the same time, Pence emphasized that the administration's efforts rendered the risk to Americans "low" -- contrary to recent statements from commentators and others, like billionaire Bill Gates, who ominously declared the coronavirus a "once-in-a-century pathogen we’ve been worried about."

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"His assessment doesn't agree with our health experts, but I agree with his generosity," Pence, whom Trump appointed to head up the White House's coronavirus task force, remarked flatly.

Pence additionally told Maria Bartiromo that there were heartening signs overseas, and that "there were actually fewer new cases in China than in the balance of the rest of the world."

Pressed on that claim, given concerns that China has been providing inaccurate numbers, Pence responded, "Well, we had CDC [Centers for Disease Control and Prevention] officials that were just in China a few short weeks ago, and they informed we that they were able to look at the raw data, and from their initial look, it did line up with much of the data that we were receiving. We'll continue to ask the hard questions; we'll continue to call on China to be even more transparent than they've been."

Pence added: "I think the president's decision to suspend all travel out of China and establish a quarantine for Americans who are returning here should tell you everything you need to know about our overall concern [about] what's happening in China."

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The vice president emphasized the possible coronavirus threat from other nations, and touted the administration's fresh new travel restrictions, which state that foreign nationals who have visited Iran in the last 14 days will not be allowed back in the United States -- and that in portions of Italy and South Korea, a Level 4 "do not travel" advisory was established.

Specifically, the administration's advisory Sunday cited quarantines set up in 10 Lombard towns and one in Veneto, with a combined population of 50,000 people, as well as ‘’the level of community transmission of the virus.'' It followed an earlier warning late Friday to avoid non-essential travel to all of Italy, where more than 1,100 cases were confirmed through Saturday along with 29 deaths.

Tourism officials have cited the previous warning covering all of Italy as potentially calamitous to the industry, which represents 13 percent of gross domestic product in a country famed for its world-class museums, archaeological sites, art cities and natural beauty.

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A similar do-not-travel warning has gone out for Daegu, South Korea, with caution to reconsider any travel to the entire country.

On Sunday, the coronavirus dramatically shut down France's Louvre Museum, with workers who guard its famous trove of artworks fearful of being contaminated by the museum's flow of visitors from around the world.

“We are very worried because we have visitors from everywhere,” said Andre Sacristin, a Louvre employee and union representative for its staffers, calling the risk "very, very, very great."

Pence additionally underscored the U.S.' recent offer to provide assistance for Iran, which the regime there has previously dismissed as "ridiculous."

The viral outbreak, which began in China, has infected more than 87,000 people globally and caused nearly 3,000 deaths, according to the latest figures from The World Health Organization. The WHO has named the illness COVID-19, referring to its origin late last year and the coronavirus that causes it.

There have been 62 cases confirmed in the U.S. with one death; overseas, there have been at least 2,870 reported deaths among 79,824 cases, and in Iran, there have been 978 cases with 54 deaths. In South Korea, 3,736 cases and 20 deaths have been reported, while in Italy, there have been 1,128 reported cases and 29 deaths. In the United Kingdom, 35 cases and 1 death have been tallied.

Concerning domestic testing, Pence revealed that "we believe we are in the process of resolving the issues about testing kits" that have been sent to states.

"Yesterday, we have now approved a new arrangement so that states can conduct these tests on their own," Pence said. "As we speak, literally more than 15,000 kits are going out to the relevant areas, and we'll soon be sending another 50,000 that are going to be made commercially available out to states."

When Bartiromo pushed back, saying only 500 people had been tested in the U.S. and that other countries allow drive-through testing or testing at home, Pence noted that "we've actually screened 47,000 people coming through designated airports in the country."

"The new challenge that we have is that we want to make testing kits available to local health care providers, so that if someone presents with a respiratory illness, they'll not only be tested for the flu, they'll also be tested for the coronavirus," Pence said.

The FDA announced Saturday it would loosen restrictions on coronavirus testing by hospitals and labs.

Earlier in the day, Health and Human Services Secretary Alex Azar exclusively told Fox News that a new case of the coronavirus appeared in Chicago overnight, marking the latest spread of the outbreak in the United States.

Speaking on "Fox News Sunday," Azar confirmed the latest infection as fears mount that the virus will continue to spread across the country.

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"We've had 23 cases here in the United States that are not a result of us repatriating individuals from Japan or China," Azar said. "Of those individuals, we've got cases in Chicago as well as Washington and Oregon where we do -- and two in California where we do not yet know why they contracted the novel coronavirus."

Fox Business Network's Maria Bartiromo, Fox News' Andrew O'Reilly, and The Associated Press contributed to this report.