A half-dozen senior health-care workers who refused to comply with a New Jersey hospital system’s coronavirus vaccine mandate have been fired, the latest example of a company taking action against those who push back against vaccine policies.

RWJBarnabas Health, the largest health-care system in the state, said in May that all team members at the supervisory level or above would be required to complete their course of coronavirus vaccinations no later than June 30. The idea was they would set an example for other staff members, and the state’s residents, in fighting the spread of the coronavirus.

The vast majority — 99.7 percent — complied and were fully vaccinated or had received a medical or religious exemption, or a deferral, the company said in a statement Wednesday. Six did not and are no longer employees of the company, the hospital group said.

News of the New Jersey dismissals comes after a coalition of health-care organizations Tuesday called on medical facilities to require their workers to be immunized against the virus, saying the strategy has worked to fight influenza and other infectious diseases and is necessary to contain the pandemic.

In June, Houston Methodist — one of the first health systems to require the coronavirus shots — dismissed or accepted the resignations of 153 workers who didn’t comply with the Houston-based hospital system’s vaccine mandate.

That mandate had been challenged in a lawsuit brought by employees, including Jennifer Bridges, a former nurse who alleged the policy was unlawful and forced staffers to be “guinea pigs” for vaccines that had not gone through the full Food and Drug Administration approval process. A federal-district court judge dismissed the lawsuit last month.

The FDA has authorized three coronavirus vaccines for emergency use, following rigorous clinical trials involving tens of thousands of people, and U.S. firms Moderna and Pfizer, with German partner BioNTech, have applied for full approval for their vaccines.

A number of health systems, including in Maryland and the District, have moved to require coronavirus vaccines for their employees. But federal officials have resisted imposing national requirements on health-care workers, and many health-care organizations have said they do not plan to require their staff members to get vaccinated.

The New Jersey-based hospital system didn’t name the employees who were fired, or say where they worked.

RWJBarnabas Health covers nine counties with 5 million people, and includes 11 acute-care hospitals, according to the company website. It is New Jersey’s largest private employer, with more than 35,000 staffers, 9,000 physicians, and 1,000 residents and interns. The company said it will be announcing mandatory plans to vaccinate all nonsupervisory staff and physicians in the coming days.

Since the start of the pandemic, New Jersey has recorded more than 1 million coronavirus cases and more than 26,000 deaths, according to Johns Hopkins University data. About 58 percent of the state’s 8.9 million residents are fully vaccinated, putting it ahead of the national vaccination rate of 49 percent.