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CAMBRIDGE, England — Amid an outbreak of measles that has spread across 14 states, Gov. Chris Christie of New Jersey on Monday said that parents “need to have some measure of choice” about vaccinating their children against the virus, breaking with President Obama and much of the medical profession.

In remarks here, Mr. Christie at first stopped short of recommending that parents immunize their children against measles, or any other illness, calling for “balance” and “choice.” But his remarks quickly set off an outcry, prompting the governor to modify his position about an hour later and declare, through a spokesman, that “there is no question kids should be vaccinated.”

Mr. Christie, when asked about the connection between the new measles cases and parents who object to the long-recommended vaccine against it, said that he and his wife had vaccinated their four children. He called that “the best expression I can give you of my opinion.”

But he added: “It’s more important what you think as a parent than what you think as a public official. 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.”

Mr. Christie said that “not every vaccine is created equal, and not every disease type is as great a public health threat as others.”

Mr. Obama on Sunday night issued an unambiguous call for parents to have their children vaccinated. He called the scientific rationale for using the vaccines “pretty indisputable.”

Mr. Christie did not offer any such urgency or firmness in his original remarks. That prompted a scolding response from the White House. Mr. Obama’s senior adviser, Dan Pfeiffer, took to Twitter to request that Mr. Christie “clarify” his statement. “It’s important that responsible leaders speak with one voice,” Mr. Pfeiffer wrote.

Doctors warn that up to 1,000 people may have been exposed to measles in recent weeks, a risk linked to parents who, against the advice of the medical profession, refuse to vaccinate their children for a variety of reasons.

Mr. Christie spoke during an impromptu news conference in front of a facility for MedImmune, an American company that makes a nasal flu vaccine, called FluMist. Inside, Mr. Christie donned a lab coat and protective plastic goggles.

He is traveling in the London area on a three-day trade mission.