CHICAGO (Reuters) - The vast majority of U.S. kindergarten-age children are vaccinated against preventable diseases but sizable pockets of unprotected children still exist, posing a public health threat, according to a government study.

Only 1.7 percent of U.S. parents of kindergartners sought exemptions in 2014 from laws requiring children be vaccinated, according to the U.S. Centers for Disease Control and Prevention study.

Rates vary nationwide, however, with at least one state reporting over 6 percent of parents seeking exemptions, the study released Thursday found.

"Pockets of children who miss vaccinations exist in our communities and they leave these communities vulnerable to outbreaks of vaccine-preventable diseases," Dr. Anne Schuchat, director of the CDC's National Center for Immunization and Respiratory Diseases, told reporters in a media briefing.

Lawmakers in at least 10 states including California are making efforts to tighten school vaccination exemption rules after a measles outbreak at Disneyland in Anaheim sickened more than 100 people earlier this year.

All states require a schedule of vaccines that a child must have before he or she can be enrolled in school. Every state allows exemptions from vaccines for medical reasons, and all but Mississippi and West Virginia allow exemptions for religious reasons.

Because U.S. measles vaccination rates are high, at 94 percent among kindergarten-age children, the Disney outbreak was less of a problem than in Canada, Schuchat said.

"We were lucky in the U.S. We didn't see large outbreaks in schools," she said, adding that in one province in Canada, there were more than 100 measles cases from the Disney exposure "because of a big pocket of undervaccinated people."

High vaccination rates provide herd immunity, preventing the spread of a virus to individuals too young or too sick to be vaccinated.

According to the report, which included data on 45 states that met reporting requirements and the District of Columbia, the median rate of kindergartners with any exemption was less than 1 percent in six states and greater than 4 percent in 11 states.

Mississippi reported the lowest rates of vaccine exemptions with a median of 0.1 percent, while Idaho reported the highest at 6.5 percent.

Schuchat said she was encouraged that states increasingly are making vaccination coverage information available to residents online, with as many as 21 states doing so in the current reporting period.

Parents can use that data to check on vaccination coverage in their own communities and schools, depending on how the state reports the data, she said.

(Reporting by Julie Steenhuysen; Editing by Andrew Hay)