New Jersey Gov. Chris Christie said Monday parents should have some choice on whether to vaccinate their children, a position he's taken before but one that drew a new level of attention amid a U.S. measles outbreak and his recent moves toward running for president.

The political significance of Christie's remarks was amplified by his office a short time later, when it released a statement saying the governor believes "with a disease like measles there is no question kids should be vaccinated."

Christie's stumble into the vaccine issue came as a measles outbreak centered in California has sickened more than 100 people in several states and Mexico, putting a new spotlight on parents who choose not to vaccinate their children. Some do so for religious or philosophical reasons, while others cite a concern that vaccines can lead to autism and developmental disorders — a link debunked by rigorous medical research.

Christie found an ally in fellow Republican White House prospect, Kentucky Sen. Rand Paul, who said in a Monday radio interview that most vaccines should be voluntary.

"I have heard of many tragic cases of walking, talking, normal children who wound up with profound mental disorders after vaccines," Paul, an eye doctor, said in a subsequent interview while suggesting vaccines were "a good thing." ''But I think the parents should have some input. The state doesn't own your children."

His staff, too, sent out a clarifying statement afterward, saying that Paul "believes that vaccines have saved lives, and should be administered to children. His children were all vaccinated."

Hillary Rodham Clinton, the leading Democratic contender for the party nomination in 2016, couldn't resist taking a dig at the GOP hopefuls on Twitter.

"The science is clear: The earth is round, the sky is blue, and #vaccineswork. Let's protect all our kids. #GrandmothersKnowBest."

Christie, a Republican who recently launched an organization that allows him to raise money for a possible 2016 presidential campaign, was asked about the outbreak after touring a facility operated by MedImmune, which manufacturers the flu vaccine FluMist. Christie is on a three-day trip to the United Kingdom.

He said that he and his wife had vaccinated their children, describing that decision as "the best expression I can give you of my opinion." He said they believe doing so is an "important part of making sure we protect their health and the public health."

"But," Christie added, "I also understand that parents need to have some measure of choice in things as well. So that's the balance that the government has to decide."

It's not a new position for Christie, who during his first campaign for governor in 2009 pledged to fight for greater parental involvement in vaccination decisions.

All states now require children to get certain vaccinations to enroll in school, although California and New Jersey are among 20 states that let parents opt out by obtaining a waiver. Parents in New Jersey seeking such a waiver for medical reasons must submit a written statement from their doctor or registered nurse.

The American Academy of Pediatrics strongly urges parents to get their children vaccinated against measles and other childhood diseases. The New Jersey health department's guidelines on vaccines say that objections "based on grounds which are not medical or religious in nature and which are of a philosophical, moral, secular, or more general nature continue to be unacceptable."

Concerns about autism and vaccinations are often traced to a 1998 study in the British journal Lancet. While the research was later discredited and retracted by the journal, legions of parents abandoned the vaccine, leading to a resurgence of measles in Western countries where it had been mostly stamped out. Last year, there were more than 4,100 cases in Europe, according to the European Centre for Disease Prevention and Control.

President Barack Obama, asked about the outbreak this weekend, said in an interview with NBC News that all parents should get their kids vaccinated. Those children who are not, he said, put infants and those who can't get vaccinations at risk.

"I understand that there are families that, in some cases, are concerned about the effect of vaccinations," Obama said. "The science is, you know, pretty indisputable."

Measles is a highly contagious disease that spreads through the air, with symptoms that include fever, runny nose and a blotchy rash. The measles-mumps-rubella vaccine is 97 percent effective at preventing measles, according to the Centers for Disease Control and Prevention.

"Choosing not to vaccinate your child could also endanger the health of other children in your community," CDC director Tom Frieden said Monday.

New Jersey requires the vaccine for children between 12 months and 15 months old, and then a second dose between ages 4 and 6. Such mandated vaccinations are a point of irritation among some conservatives, notable in the early voting state of Iowa, where Christian home-school advocates constitute an influential bloc of voters who take part in the Republican presidential caucuses.

Barb Heki, a leader in Iowa's home-school advocacy network, said such parents "adhere to the idea that it's the parents' right to make the decision on vaccinations.

"More important than a candidate's stance on vaccinations, I'm more concerned for parents' rights to make decisions about their own children, period," she said. "That's paramount."

Louise Kuo Habakus, a radio host who runs a nonprofit group opposed to state-required vaccinations, said she helped arrange a meeting between parents and Christie on the issue in 2009 and saluted him for standing up for the "rights of parents to direct the health, welfare and upbringing of their children."

"He's been absolutely constant and I believe courageous and principled on this issue," she said.

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