HOUSTON — Day after day, Adonias Arevalo tried to calm his parents’ nerves, attempting to convince them it was safe for him to apply for government-subsidized health insurance through the nation’s new coverage system.

Like many other immigrants, Arevalo’s parents worried that personal information on their son’s application could somehow draw immigration authorities’ attention to the couple, who emigrated here illegally from El Salvador seven years ago.

After a week of discussion, the 22-year-old Houston man, who works at a community center and has temporary legal status, finally eased their fears. But other immigrant families remain leery, and some are so concerned that they would rather see loved ones go without coverage than risk giving personal information to a federal agency.

“They are afraid,” Arevalo said. “The majority of families, they know it’s something they need to do. … They’re just afraid of putting themselves out like that.”

Immigrants who are in the U.S. illegally cannot participate in the system. But many have eligible relatives who are citizens or legal residents.

Since the system debuted in October, immigrant advocates and the federal government have been working to reassure families that their information will not be shared with enforcement agencies. The effort has led to changes in the main health care website and a memo from immigration authorities promising not to go after anyone based on insurance paperwork.

Immigrant families are important to the success of the health care overhaul, especially in Texas, which has the nation’s highest rate of uninsured people, many of whom are immigrants.

Of the nearly 40 million people living in the U.S. who were born elsewhere, about a third do not have health insurance, according to census data. And about 9 million people in the U.S. belong to immigrant families in which at least one child is a citizen, according to the Pew Research Center’s Hispanic Trends Project.

Those immigrant families, which tend to be younger and healthy, are attractive to the health care program because it relies on young participants to pay premiums to help fund coverage for older people who need more expensive care.

In Houston’s Harris County, where more than a quarter of the 4 million residents are foreign-born, the group Enroll America is trying to soothe anxieties that signing up for insurance could mean risking deportation.

“It has pushed people away from wanting to apply online,” said Mario Castillo, who leads the group’s efforts in the Houston area. “They don’t want to type that into a computer … they want to put a paper application in.”

Cheryl O’Donnell, state director of Enroll America in Arizona, said her staff is confronting similar concerns.

“There is a lot of fear, particularly if the noncitizen is applying for a citizen child,” she said.

In mid-October, three weeks after enrollment opened, President Barack Obama’s administration stepped in. Immigration and Customs Enforcement published a “clarification” designed to assuage fears. The memo explained that information obtained through health care registration would not be used to pursue immigration cases against anyone in the country illegally.

Jenny Rejeske, a health policy analyst at the National Immigration Law Center, said advocates had shared with the government concerns they heard from mixed-status families.

Advocates had sought that clarification for years, but it wasn’t until federal officials “saw that this was going to be a deterrent for people applying that they decided to do something about it,” Rejeske said.

Around the same time, a new page appeared on healthcare.gov titled “What do immigrant families need to know about the marketplace?” Under a heading for mixed-status families, it states: “Family members who aren’t applying for health coverage for themselves won’t be asked if they have eligible immigration status.”

It also said that applying to the insurance marketplace, Medicaid or the children’s program known as CHIP will not mean immigrants are considered a “public charge,” addressing a long-held concern that accepting a government benefit could jeopardize their chance of getting legal status or becoming a naturalized citizen.