Dozens of groups representing doctors, nurses and other medical workers called on their employers to mandate Covid-19 vaccination among employees in healthcare facilities, as the Delta variant pushes up hospitalizations in much of the country.

About 60 groups including the American Nurses Association, the American Medical Association, Infectious Diseases Society of America and the American Academy of Pediatrics said unvaccinated healthcare workers are putting their patients and residents of long-term-care facilities at risk for infection.

“Vaccination is the primary way to put the pandemic behind us,” the groups said in a statement on Monday.

The drive to vaccinate Americans against Covid-19 has been stalled for weeks, with about 57% of eligible people having completed their course of inoculation.

A recent survey by the American Medical Association found that 96% of physicians have been fully vaccinated against Covid-19, but among healthcare workers overall, a recent analysis of U.S. Department of Health and Human Services data found that one in four hospital workers with direct contact with patients hadn’t received a dose of vaccine by the end of May.

More than a dozen hospital systems have said in recent months they would require the shots, including major hospital systems in Missouri and Michigan, states where less than half the total population is fully vaccinated.

In some of those states, Covid-19 cases have risen sharply in recent weeks, driven by the highly contagious Delta variant, which now dominates new infections in the U.S. Most patients driving up Covid-19 hospitalizations in parts of the U.S. are unvaccinated, hospital executives and local officials have said.

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Write to Julie Wernau at Julie.Wernau@wsj.com