New Jersey Gov. Chris Christie and his wife Mary Pat Christie visit a MedImmune laboratory in Cambridge on Monday. (Neil Hall/Reuters)

Medical experts reacted with alarm Monday as two top contenders for the Republican presidential nomination appeared to question whether child vaccinations should be mandatory — injecting politics into an emotional issue that has taken on new resonance with a recent outbreak of measles in the United States.

First, New Jersey Gov. Chris Christie, while visiting a vaccine laboratory here, called for “some measure of choice” on whether shots guarding against measles and other diseases should be required for children.

[Christie breaks with Obama over the measles vaccine, then walks back his comments]

Then, Sen. Rand Paul (R-Ky.), an ophthalmologist who is also readying a 2016 campaign, said in two U.S. television interviews that he thinks most vaccines should be voluntary, citing “many tragic cases of walking, talking, normal children who wound up with profound mental disorders after vaccines.”

“The state doesn’t own your children,” Paul said on CNBC, praising vaccines for their health benefits but insisting that the government should not mandate their use in most cases. “Parents own the children. And it is an issue of freedom and public health.”

During a news conference, Speaker of the House John Boehner (R-Ohio) weighed in on the president's proposed budget and the debate over measles vaccinations. (AP)

The vigorous outcry in response to the remarks underscored the sensitivity surrounding the vaccination debate, particularly given a widening multistate measles outbreak linked to a California theme park. Both Christie and Paul are leading GOP candidates who are likely to exercise significant influence over the direction of the 2016 primary race.

The comments also illustrated persistent strains of skepticism within both parties over vaccination requirements, fueled in part by discredited claims of a connection between childhood shots and autism. Scientists have blamed a small but influential anti-vaccine movement for helping spark a new epidemic of measles, which was once virtually eliminated.

[Related: Everything you wanted to know about measles and the debate over vaccines]

On Monday, the Centers for Disease Control and Prevention said that more than 100 cases of the highly infectious disease were diagnosed in January. Most of the cases appear linked to victims who became ill after visiting Disneyland in Anaheim, Calif., in mid-December.

“When you see educated people or elected officials giving credence to things that have been completely debunked, an idea that’s been shown to be responsible for multiple measles and pertussis outbreaks in recent years, it’s very concerning,” said Amesh Adalja, an infectious-disease physician at the Center for Health Security at the University of Pittsburgh. He called the comments from Paul particularly troubling because Paul is a doctor.

Christie’s aides quickly tried to clarify his remarks, insisting in a statement that the Republican governor believes vaccines are “an important public health protection.”

After visiting a MedImmune vaccine laboratory in Cambridge, Christie was asked to weigh in on the debate in the United States over the measles outbreak. President Obama told NBC News anchor Savannah Guthrie on Sunday, “You should get your kids vaccinated.”

“The science is, you know, pretty indisputable,” Obama said. “We’ve looked at this again and again. There is every reason to get vaccinated, but there aren’t reasons to not.”

[ Related: Vox got it wrong when it said Obama “pandered to anti-vaxxers in 2008” ]

Christie, however, said Monday that “there has to be a balance, and it depends on what the vaccine is, what the disease type is, and all the rest.” He added: “Not every vaccine is created equal, and not every disease type is as great a public health threat as others.

“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,” he said.

As for Paul, he told talk show host Laura Ingraham that he had chosen to hold off on vaccinating his children for some diseases.

“I didn’t like them getting 10 vaccines at once, so I actually delayed my kids’ vaccines and had them staggered over time,” he said.

Both men’s remarks drew immediate rebuke from experts on the issue.

[Related: The saddest story Roald Dahl ever wrote is about his daughter’s death from measles]

Seth Mnookin, a professor at MIT who has written a book on the vaccination debate called “The Panic Virus,” called the comments from Christie and Paul “incredibly, in­cred­ibly irresponsible.”

Such remarks, he said, “basically fail at the first duty of a politician, which is to calm his constituents in moments of irrational crisis.”

The criticism came too from some political strategists, who wondered whether Christie in particular might have been attempting to appeal to Republicans suspicious of government mandates.

“There’s only one of two options,” said Rick Wilson, a Republican operative from Florida. “Either he’s so tone-deaf that he doesn’t understand why saying this is bad for him, or this is a considered political strategy. And that would be even more troubling.”

Christie aides said he was not questioning science, and they acknowledged that his initial comments could be misconstrued.

“The Governor believes vaccines are an important public health protection and with a disease like measles there is no question kids should be vaccinated,” said a statement issued from Christie’s office in Trenton, N.J., after the uproar. “At the same time different states require different degrees of vaccination, which is why he was calling for balance in which ones government should mandate.”

In substance, Christie’s overseas comments did not differ dramatically from remarks he has made previously in New Jersey, which faces higher than average childhood autism rates and an active community of parents who have questioned vaccinations.

In 2009, Christie met with parents concerned about autism rates and listened to some who expressed fears that the disease might be linked to vaccinations, said Louise Kuo Habakus, who co-edited a book called “Vaccine Epidemic” and is active with the group New Jersey Coalition for Vaccination Choice. She said not everyone at the meeting held that view.

Habakus said she gave Christie a copy of her book just before a 2011 town-hall meeting. During the public event that followed, Christie chose to call on her to ask a question, which she said she took as a sign that he wanted to allow her a forum to express her concerns.

She praised Christie for supporting “greater dialogue” about parental rights but said she had never heard him link autism and vaccination or discourage parents from getting shots for their children.

“I think he’s been very brave on this issue,” she said. “He’s been constant and courageous on this issue, saying parents should be more involved in the discussion.”

The link between vaccinations and autism was alleged in a small 1998 study that has since been widely discredited in the scientific community. The journal that published the study retracted it in 2010, and its author lost his medical license.

But many doctors had cast doubt on the study even before those actions, insisting that the measles, mumps and rubella vaccine was safe and effective at combating once-deadly but now preventable diseases.

Both Obama and Sen. John McCain (R-Ariz.) drew fire in 2008 for seeming to give credence to the link. At one campaign appearance, Obama noted that “some people are suspicious” that skyrocketing rates of autism might be linked to vaccines.

“The science right now is inconclusive, but we have to research it,” he said.

McCain said at a town hall meeting in 2008 that there was “strong evidence that indicates it’s got to do with a preservative in vaccines.”

Obama has said recently that the science is now settled and has urged vaccination.

Nick Gillespie, editor in chief of the libertarian magazine Reason, said there is a vigorous debate over vaccines, particularly whether government should mandate their use. He said Christie may have been trying to curry favor with libertarian-leaning Republicans with his emphasis on parental choice.

“There is a broadly ascending libertarian sentiment in the Republican Party,” he said. “Even mainstream establishment Republicans understand they need to speak to the libertarian wing.”

Former Hewlett-Packard chief executive Carly Fiorina, who is considering a long-shot 2016 run, also appeared to endorse parental choice for vaccines in a BuzzFeed interview last week.

“I think vaccinating for measles makes a lot of sense. But that’s me. I do think parents have to make those choices. I mean, I got measles as a kid. We used to all get measles,” she said. “I got chicken pox, I got measles, I got mumps.”

Fiorina also drew a distinction between the measles vaccine and one intended to combat human papillomavirus (HPV), a common sexual infection that can lead to cervical cancer. The vaccine sparked controversy in the 2012 campaign when then-Rep. ­Michele Bachmann (R-Minn.) blasted then-Texas Gov. Rick ­Perry for helping to institute a mandate requiring most girls in Texas to get the vaccine.

Some social conservatives object to a mandate because they argue it would suggest to young girls that having sex is acceptable. Bachmann later falsely suggested that the HPV vaccine might cause mental retardation.

Mnookin said various studies have tried to examine the political leanings of those who oppose vaccination, finding that they are drawn from both parties.

“It’s not a homogenous group,” he said. “People who don’t vaccinate are not more likely to congregate politically one side of the aisle or the other.”

Helderman reported from Washington.