A third farmworker in the United States has been found to be infected with bird flu, heightening concerns about an outbreak among dairy cattle first identified in March.

The worker is the first in this outbreak to have respiratory symptoms, including a cough, sore throat and watery eyes, which generally increase the likelihood of transmission to other people, federal officials said on Thursday.

The other two people had only severe eye infections, possibly because of exposure to contaminated milk.

All three individuals had direct exposure to dairy cows, and so far none has spread the virus to other people, Dr. Nirav Shah, principal deputy director of the Centers for Disease Control and Prevention, said at a news briefing.

That suggests that the virus, called H5N1, has not acquired the ability to spread among people and that the threat to the general public remains low, Dr. Shah said.

“This newest case does not change the C.D.C.’s H5N1 influenza risk assessment level for the general public,” he added. “We should remain alert, not be alarmed.”

But the case does highlight the ongoing risk to farm workers, Dr. Shah said: “Our top priority now across this response is protecting the health of farmworkers.”

This case is the second in Michigan, but the individual worked on a different farm than did the worker diagnosed last week. All three infected people so far have been treated with the antiviral medication oseltamivir, sometimes marketed as Tamiflu, officials said.

There were few other details available, disappointing some experts.

“There is no excuse for the lack of testing, transparency and trust,” said Rick Bright, the chief executive of Bright Global Health, a consulting company that focuses on improving responses to public health emergencies.

He noted that federal officials are “months behind sharing virus sequence data.”

“This is how pandemics start,” he said.

The identification of a third case is not surprising because farm workers interact closely with dairy cows, experts said. New flu viruses often provoke respiratory symptoms without further spread to other people, Dr. Shah said.

This latest patient may have had different symptoms because of the exposure dose, a different exposure route, predisposing genetic or medical factors or a combination of those attributes, said Angela Rasmussen, a research scientist at the Vaccine and Infectious Disease Organization at the University of Saskatchewan in Canada.

Still, gaining more information about how the person was infected, and about whether the virus has evolved to infect people more readily, is crucial, she said.

Genetic analysis of the virus infecting the worker may be difficult because the amount obtained from the patient was very low.

“But every time the virus is able to replicate in a person, there is potential for the virus to adapt to humans and gain molecular features for replication in the respiratory tract and to spread person-to-person,” said Seema Lakdawala, a virologist at Emory University in Atlanta.

Officials are monitoring about 350 people who may have been exposed, about 220 of them in Michigan alone. So far relatively few farmworkers, about 40, have consented to testing.

The Agriculture Department announced on Thursday that it was setting aside $824 million in new funding to quickly detect cases in poultry and livestock. The department is also starting a voluntary program for producers to test bulk milk, enabling them to transport virus-free herds across state lines without having to test individual cows.

Federal researchers have completed their analysis of 109 beef samples, and found virus in just one, reported last week, officials said at the briefing.

Federal officials could be doing more to protect farm workers and the public, experts said.

“Vaccines from the national stockpile should be released for veterinarians and dairy farm workers willing to take it,” Dr. Lakdawala said. “We have an opportunity to reduce human infections and we need to do it now.”