An unvaccinated person who died in New Mexico has tested positive for measles, state health officials said on Thursday, possibly the second such fatality in a growing outbreak that began in West Texas.

The officials have not yet confirmed that measles was the cause of death, and said the person did not seek medical treatment before dying.

The announcement came a little over a week after a child died of measles in Gaines County, Texas, the first such death in the United States in 10 years.

Ten cases of measles, six adults and four children, have been reported in Lea County, N.M., which borders Gaines County, the epicenter of the West Texas outbreak.

This outbreak has been a trial by fire of the new secretary of health and human services, Robert F. Kennedy Jr., a prominent vaccine skeptic. His equivocal response has drawn harsh criticism from scientists, who say he has offered muted support for vaccination and has emphasized untested treatments for measles like cod liver oil.

Instead of broadly lauding the safety and efficacy of vaccines, as past H.H.S. secretaries did, Mr. Kennedy has said that vaccines help protect against measles but that the decision to vaccinate “is a personal one.”

All the New Mexico cases have involved someone unvaccinated or with unknown vaccine status. While the cases in New Mexico have not officially been connected to the Texas outbreak, officials have said a link is “suspected.”

As of Tuesday, the measles outbreak in West Texas had sickened nearly 160 people, with 22 hospitalized.

New Mexico health officials urged residents to get the measles, mumps and rubella vaccine, which experts say is the best way to protect against the disease. Two doses of the vaccine prevent more than 97 percent of measles infections.

“We don’t want to see New Mexicans getting sick or dying from measles,” Dr. Chad Smelser, a state epidemiologist, said in a news release.

The measles virus, which spreads when an infected person breathes, coughs or sneezes, is extremely contagious. Each infected person can spread the pathogen to as many as 18 others.

Within a week or two of being exposed, those who are infected may develop a high fever, cough, runny nose and red, watery eyes. Within a few days, a telltale rash breaks out, first as flat, red spots on the face and then spreading down the neck and torso to the rest of the body.

In most cases, these symptoms resolve in a few weeks. But in rare cases, the virus causes pneumonia, making it difficult for patients, especially children, to get oxygen into their lungs.

The infection can also lead to brain swelling, which can cause lasting damage, including blindness, deafness and intellectual disabilities.

For every 1,000 children who get measles, one or two will die, according to the Centers for Disease Control and Prevention.

The virus also weakens the immune system in the long term, making its host more susceptible to future infections.

A 2015 study found that before the M.M.R. vaccine was widely available, measles might have been responsible for up to half of all infectious disease deaths in children.