ANGERS, France — The relentless whir of machines echoing across a cavernous French factory floor this week is an unexpected result of the deadly virus that has nearly paralyzed cities in China and other parts of Asia. The company, Kolmi Hopen, happens to make an item that is suddenly one of the world’s hottest commodities: the medical face mask.

The factory, in Angers, typically makes around 170 million masks a year, but in the last week orders arrived for a staggering half a billion, flooding the sales department’s inboxes at the rate of one every two minutes. Kolmi Hopen is racing to hire more workers to keep the machines running 24 hours a day, seven days a week.

“We’re making masks as fast as we can,” said Guillaume Laverdure, the chief operating officer of Kolmi Hopen’s parent company, Canada-based Medicom, as forklift drivers moved boxes of freshly finished masks into trucks.

“But demand is still rising,” he added.

The coronavirus outbreak has set off a run on protective masks across China and in other major cities. To curb the spread of the virus, the Chinese government has ordered citizens to don masks every time they go outside. Medical professionals say once used, a mask must be replaced with a fresh one, driving an explosion in demand. Grim scenes of people lined up for hours to get a protective face covering, only to be turned away when pharmacies run out, have become familiar.

“I can’t find a single mask to buy,” Sandy Lo, 60, said in Hong Kong. “I don’t know what stores have stock any more.” She said she reuses old masks, “because what else could I do?”

Most of the world’s face masks are made in China and Taiwan. But factories there, including ones run by Medicom, have been forced to temporarily halt exports to comply with government demands to reserve them for frantic residents.

On Monday, the Chinese government, conceding that it was in urgent need of medical masks and other protective gear, said it would begin importing them from Europe, Japan and the United States to help make up for the shortfall.

It has made the Kolmi Hopen outpost in western France an unlikely hot spot. Phones at the factory have been ringing off the hook as medical supply buyers scour the globe for mask makers.

Demand is especially strong for high-filtration respiratory masks, which can be more effective against the spread of virus-laden droplets than surgical masks, Mr. Laverdure said. Another Medicom factory that makes face masks, in Augusta, Ga., is also ramping up production. Mr. Laverdure declined to discuss financial details, including the cost of the masks.

Scientists say there isn’t much evidence that masks actually protect healthy people. (Hand washing may be more important.) Still, as the coronavirus spreads, with thousands of confirmed cases and hundreds of deaths, experts fear that supplies of face masks and other sanitary protection items will run low in other countries — even for routine medical use. Pharmacies in the United States have begun reporting shortages.

The frenzy of orders at Kolmi Hopen shows the large-scale disruption that China can create in the global supply chain for even the most specialized products, if factories there fail to operate at full strength.

China alone produces about half the world’s sanitary face masks — around 20 million a day, or more than seven billion a year, supplying hospitals and medical workers in numerous countries. Taiwan makes up 20 percent of the global supply.

Production had already slowed as Chinese factories wound down for the Lunar New Year holiday in early January. Some sites around Wuhan, the epicenter of the coronavirus outbreak, have yet to fully revive production and are operating at around 60 percent capacity, according to the government.

Medicom’s factory in Wuhan, which makes surgical gowns, is among those that have delayed reopening. The company’s mask-making site in Taiwan is no longer allowed to export. And at Medicom’s Shanghai factory, the government sent in monitors and is requisitioning the three million masks produced daily as they roll off the production line, Mr. Laverdure said.

Supply shortages could be made worse by the fact that parts for masks and respirators are made in a variety of countries. More than 90 percent of surgical masks sold in the United States are produced overseas, according to the Department of Health and Human Services. Parts — or sometimes the final assembly — may be based not only in China and Taiwan but also in Japan, Vietnam, Mexico and Colombia.

“These countries could easily cut off our supply chain,” said Laurie Garrett, a policy expert and Pulitzer Prize-winning reporter who has written about the SARS, Ebola and other outbreaks.

With China’s pipeline to the outside world running dry, medical suppliers around the globe, including giants like Honeywell and 3M, are scrambling to find alternative sources. Both companies said through representatives that they were experiencing a surge in demand and were moving to ramp up production wherever they could.

Prestige Ameritech, a mask manufacturer in North Richland Hills, Texas, is among companies that received international orders as the coronavirus spread to 24 countries in the last few weeks, including from the governments of Hong Kong, Singapore and Taiwan.

“I have thousands of emails from people in Asia,” said Mike Bowen, the executive vice president. “Last week I sent over a million masks to China. That’s one thing I never predicted, that I’d be sending masks to China.”

Even the smallest producers are caught in the surge.

Pardam, a company in the Czech Republic that makes nanofibers, which trap micro-particles, almost ditched a sanitary mask prototype that it had tested last year because of tepid demand. But after the coronavirus hit, Pardam sold out of its stock of 2,000 masks within two days last week, and is turning to automation to increase production, said Jiri Kus, chairman of the Czech Association of Nanotechnology Industry, speaking on behalf of Pardam.

At Medicom, officials rolled out an emergency plan this week for the Angers factory to add 30 new workers to the 100-person operation, with an eye to moving toward round-the-clock production. The company is pumping out over one million masks a day, twice the normal amount, Mr. Laverdure said.

Inside the factory, over a dozen machines assembled masks at a rate of 80 per minute, combining synthetic fibers unfurled from giant bobbins, and stamping each with nose strips, head ties or ear loops. Five machines made surgical masks, the thin rectangular pads that cover the nose and mouth, while other machines pieced together the more rugged respiratory masks.

Four workers, including two newcomers who started training this week, inspected a batch of coveted respiratory masks and stacked them into boxes that were then moved to the warehouse for shipment to Hong Kong and other destinations.

Medicom had experience grappling with the SARS, H1N1 and Ebola virus crises. As reports of the coronavirus emerged in December, executives organized a war room at headquarters in Montreal to monitor developments and game out production plans for its Europe and North American sites and at its factories in Wuhan, Shanghai and Taiwan.

“When we then saw the shutdown of the cities in China, the government extending the Chinese New Year and then halting exports of masks,” Mr. Laverdure said, “we called our factories and said: ‘An epidemic is developing. Do what you can to secure more coverage.’”

Kolmi Hopen was able to ramp up production quickly because its raw materials suppliers are based in France and nearby European countries. Still, these companies, too, have scrambled to extend factory hours and rushed to hire more workers to keep up with the demand, Mr. Laverdure said, adding, “It creates a lot of stress on the supply chain — it’s not easy to manage.”

As the Chinese government moved to create mass quarantine camps this week around the epicenter of the outbreak, the company braced for a brisker pace.

“Demand is not stopping,” Mr. Laverdure said. “The situation is evolving rapidly.”

Reporting was contributed by Knvul Sheikh and David Yaffe-Bellany from New York, Cao Li and Tiffany May from Hong Kong, and Hana de Goeij from Prague.