NEW YORK — As an outbreak of measles surges across the United States — with 704 cases this year and counting — some local health officials are trying to deal with contagion in unvaccinated communities by turning to extraordinary police powers from the past.

Not long ago, measles was thought to be a problem that was mostly solved. The once-common disease became increasingly rare after a vaccine became available in the 1960s. In 2000, health officials declared the disease eliminated in the U.S., meaning that all new cases stemmed from infected travelers and not from homegrown transmission.

A decade ago, the cases numbered fewer than 100 a year. But they have been jumping since then, with the worst happening right now.

On Monday, U.S. health officials said the national tally already has eclipsed the total for any full year since 1994, when 963 cases were reported.

Twenty-two states have reported cases, but the vast majority have been in New York, where most of the cases have been unvaccinated people in Orthodox Jewish communities.

The Centers for Disease Control and Prevention says this year’s count includes 44 people who caught the disease while traveling in another country. Some of them triggered U.S. outbreaks, mostly among unvaccinated people.

Measles in most people causes fever, a runny nose, cough and a rash all over the body. A very small fraction of those infected can suffer complications such as pneumonia and a dangerous swelling of the brain.

The return of measles may be an early warning sign of a resurgences of other vaccine-preventable diseases such as rubella, chickenpox and bacterial meningitis, some experts say.

In Rockland County, officials last month banned all unvaccinated children from indoor public places.

In New York City this month, officials ordered mandatory vaccinations in four Brooklyn ZIP codes, threatening possible fines of up to $1,000 for noncompliance. The city also has shut down seven religious schools that failed to exclude unvaccinated children, though five were later allowed to reopen after submitting a corrective plan.

Last week in California, more than 1,000 students and staff at two Los Angeles universities were quarantined on campus or sent home after cases began to appear.

Officials in Vancouver, Wash., declared an end Monday to a measles outbreak that began in January but apparently stopped at 71 cases a month ago. It was a much smaller community than New York City or Los Angeles and was tamed by an intense investigation and vaccination campaign that involved 230 health workers tracking down infected people and those they had contact with, at a cost of about $865,000.

Meanwhile, there is a new wave of efforts in state legislatures to end philosophical and religious exemptions to vaccination requirements in schools.