WASHINGTON — A global arms race for a coronavirus vaccine is underway.

In the three months since the virus began its deadly spread, China, Europe and the United States have all set off at a sprint to become the first to produce a vaccine. But while there is cooperation on many levels — including among companies that are ordinarily fierce competitors — hanging over the effort is the shadow of a nationalistic approach that could give the winner the chance to favor its own population and potentially gain the upper hand in dealing with the economic and geostrategic fallout from the crisis.

What began as a question of who would get the scientific accolades, the patents and ultimately the revenues from a successful vaccine is suddenly a broader issue of urgent national security. And behind the scramble is a harsh reality: Any new vaccine that proves potent against the coronavirus — clinical trials are underway in the United States, China and Europe already — is sure to be in short supply as governments try to ensure that their own people are the first in line.

In China, 1,000 scientists are at work on a vaccine, and the issue has already been militarized: Researchers affiliated with the Academy of Military Medical Sciences have developed what is considered the nation’s front-runner candidate for success and is recruiting volunteers for clinical trials.

China “will not be slower than other countries,” Wang Junzhi, a biological products quality control expert with the Chinese Academy of Sciences, said Tuesday at a news conference in Beijing.

The effort has taken on propaganda qualities. Already, a widely circulated photograph of Chen Wei, a virologist in the People’s Liberation Army, receiving an injection of what was advertised to be the first vaccine, has been exposed as a fake, taken before a trip she made to Wuhan, where the virus began.

President Trump has talked in meetings with pharmaceutical executives about making sure a vaccine is produced on American soil, to assure the United States controls its supplies. German government officials said they believed he tried to lure a German company, CureVac, to do its research and production, if it comes to that, in the United States.

The company has denied it received a takeover offer, but its lead investor made clear there was some kind of approach.

Asked by the German magazine Sport 1 about how the contact with Mr. Trump had unfolded, Dietmar Hopp, whose Dievini Hopp BioTech Holding owns 80 percent of the company, said: “I personally didn’t speak to Mr. Trump. He spoke to the company and they immediately told me about it and asked what I thought of it, and I knew immediately that it was out of the question.”

The report of the approach was enough to prompt the European Commission to pledge another $85 million to the firm, which has already had support from a European vaccine consortium.

The same day, a Chinese company offered $133.3 million for an equity stake and other consideration from another German firm in the vaccine race, BioNTech.

“There has been a global wake-up call that biotechnology is a strategic industry for our societies,” Friedrich von Bohlen, the managing director of the holding company that owns 82 percent of CureVac.

And just as nations have insisted on building their own drones, their own stealth fighters and their own cyberweapons, they do not want to be beholden to a foreign power for access to the drugs that are needed in a crisis.

After two decades of farming out drug production to China and India, “you want the whole production process close to home,” Mr. von Bohlen said.

Some experts view the geopolitical competition as healthy, as long as any successes are shared with the world — which government officials routinely assure they will be.

But they do not say how, or more important, when. And many analysts recall what happened during the swine flu epidemic in 2009, when a company in Australia that was among the first to develop a single-dose vaccine was required to satisfy demand in Australia before fulfilling export orders to the United States and elsewhere.

That spurred outrage, conspiracy theories and congressional hearings into the reasons for the shortfall.

“You want everybody to cooperate, everybody to race as quickly as they can to a vaccine and the best candidates to move forward,” said Dr. Amesh Adalja of the Center for Health Security at Johns Hopkins University.

But if those showing signs of success are wondering if their companies will be nationalized, he said, it creates a complication that “you don’t want to have when you are trying to get a vaccine made as quickly as possible.”

Executives of the world’s leading pharmaceutical companies said on Thursday that they were working together and with governments to assure that a vaccine is developed as quickly as possible and distributed equitably. But they implored governments not to hoard a vaccine once it is developed, saying that to do so would be devastating for the broader goal of stamping out the coronavirus pandemic.

“I would encourage everyone not to get into this trap of saying we have to get everything into our countries now and close the borders,” said Severin Schwan, the chief executive of the Swiss pharmaceutical company Roche. “It would be completely wrong to fall into nationalist behavior that would actually disrupt supply chains and be detrimental to people around the world.”

Adding to the pressure is Mr. Trump’s near-daily assurance that breakthroughs are on the way. While antiviral drugs to treat the effects of the coronavirus may be tested under “compassionate use” guidelines that allow experimentation on desperately ill patients, a vaccine remains at least 12 to 18 months away, both American officials and the leaders of major pharmaceutical companies say.

“Vaccines are injected into healthy people, so we need to ensure safety,” a process that takes time, David Loew, an executive vice president of Sanofi Pasteur of France, said on Thursday. His firm is working with Eli Lilly and Johnson & Johnson in the United States, Roche and Takeda in Japan.

In normal times, there is always an element of national competition to the development of drugs. In the months before the coronavirus began breaking out in Wuhan, the F.B.I. began an effort to root out scientists they believed were stealing biomedical research from the United States, mostly focused on scientists of Chinese descent, including naturalized American citizens, on behalf of China. There were 180 cases under investigation last year.

But the fear is that the urgency to come up with a usable vaccine will inflame nationalistic tendencies.

China has made clear it is looking for a national champion — an equivalent to the role that Huawei, a Chinese telecommunications giant, plays in the race to build 5G networks around the world. If the Huawei pattern holds, China could make deals to increase its influence over poorer or less developed countries, which otherwise might not get affordable access to a vaccine.

There are already signs that China is using the moment for geopolitical advantage, delivering help to countries that once would have looked to Europe or the United States. Its decision to ship diagnostic kits to the Philippines, an ally of the United States, and to help Serbia was a leading indicator of what may come with drugs and vaccines, when they are available.

Speaking in a teleconference on Thursday, executives from the five biggest pharmaceutical companies said they were working to increase the industry’s manufacturing abilities by sharing available capacity to ramp up production once a successful vaccine or antiviral is identified. They argued for multiple testing programs to increase the chances of success, and then for immediate licensing to allow a quick scaling up of production.

Once a vaccine is approved, “we’ll need to vaccinate billions of people around the world, so we are looking at alternatives to where and how we produce,” Mr. Loew said.

But it is governments that get to decide how a vaccine is approved, and where it can be sold.

“If countries say, ‘Gee, let’s try to lock up a supply so we can protect our populations,’ then it can be a challenge to get the vaccine to the places where it can make the most difference epidemiologically,” said Seth Berkley, the chief executive of GAVI, a nonprofit organization that supplies vaccines to developing countries.

Mindful of those dangers, though, several European governments and nonprofit groups have already taken steps to prevent either the United States or China from capturing a monopoly on a potential vaccine against the coronavirus.

In the aftermath of the Ebola plague that flared across West Africa from 2014 to 2016, Norway, Britain and other mostly European countries as well as the Bill and Melinda Gates Foundation began contributing millions of dollars to a multinational organization, the Coalition for Epidemic Preparedness Initiatives, to fund vaccine research.

All of its funding agreements included provisions for equal access to assure that “appropriate vaccines are first available to populations when and where they are needed to end an outbreak or curtail an epidemic, regardless of ability to pay,” the organization said in a statement.

In the past two months, the coalition has funded research into eight of the most promising candidates to block the coronavirus — including CureVac, the Germany company.

All of which left unclear exactly what Mr. Trump sought from CureVac, if anything, and why the company ousted its American chief executive, Daniel Menichella, days after he met with the White House coronavirus task force, in a session where Mr. Trump dropped by. The White House declined to comment.

The company itself has issued carefully drafted denials of a takeover offer. “Maybe someone said something,” Mr. Von Bohlen said. “But there is no written offer from the United States.”

There did not need to be. The mere hint of it was enough to get European officials to offer more funding.

“The fact that other countries tried to buy that company shows that they are the front-runner in the research,” said Ursula von der Leyen, the president of the European Commission. “It is a European company — we wanted to keep it in Europe, it wanted to stay in Europe. It was very important to give it the necessary funding, and that has happened.”

David E. Sanger reported from Washington, David D. Kirkpatrick from London, Sui-Lee Wee from Singapore and Katrin Bennhold from Berlin. Liz Alderman contributed reporting from Paris, and Michael D. Shear from Washington.