The vaccination exemption rate among kindergarten students in California — cases in which parents said they did not want their children vaccinated for health, religious or other reasons — was 3.1 percent in the 2013-14 school year, according to the C.D.C. report. Oregon had an exemption rate of 7.1 percent, the nation’s highest, the report found. Health officials said the vaccination rate needed to be above 95 percent in all communities to prevent outbreaks.

Still, the California figure can be deceiving. Health officials said there were pockets across the state, including wealthy neighborhoods in Los Angeles and Orange Counties and enclaves in Northern California, where the exemption rate jumped into the double digits. California has long been viewed as particularly prone to this kind of outbreak because of its population size and the number of people arriving from overseas.

“The problem is that there are these pockets with low vaccination rates,” said Dr. Jane Seward, the deputy director of the viral diseases division at the C.D.C. “If a case comes into a population where a lot of people are unvaccinated, that’s where you get the outbreak and where you get the spread.”

Organizations that have led the campaign of doubts about vaccinations suggested that it was too soon to draw such a conclusion. The groups cautioned parents not to be pressured into having their children receive vaccinations, which the organizations say have been linked to other diseases. Health professionals say those claims are unfounded or vastly overstated.

“It’s premature to blame the increase in reports of measles on the unvaccinated when we don’t have all the facts yet,” said Barbara Loe Fisher, the president of the National Vaccine Information Center, a group raising concerns about inoculations. “I do know this: Fifty-seven cases of measles coming out of Disneyland in a country with a population of 317 million people is not a lot of cases. We should all take a deep breath and wait to see and get more information.”

A handful of doctors seem sympathetic to these views. Dr. Jay Gordon, a Santa Monica pediatrician who has cautioned against the way vaccines are used, said he had “given more measles vaccines” than ever before but did not like giving the shot to younger children.