Britons are increasingly worried that U.S. concerns over British Prime Minister David Cameron's quarrel with the European Union may lead to major differences with Washington over international diplomacy and strategy.

Much of the recent airing of U.S. views on Cameron's stance on British EU membership has come secondhand or through indirect or diplomatically understated quotes.

But the U.S. comments have spotlighted for Britons an uncomfortable truth: the much trumpeted U.S.-U.K. "special relationship" cannot be at the expense of U.S. ties with the European Union, its large economies and emerging military prowess independent of NATO.

U.S. Assistant Secretary of State for European Affairs Phil Gordon said the United States enjoyed "a growing relationship with the EU as an institution, which has an increasing voice in the world, and we want to see a strong British voice in that EU.

"That is in America's interests," Gordon said. "We welcome an outward-looking EU with Britain in it."

A White House statement echoed Gordon's comments and left no doubt in the minds of British audiences, as media analyses and comment showed, that U.S. President Barack Obama values Britain's position within Europe and wants that relationship to continue.

"The president underscored our close alliance with the United Kingdom and said that the United States values a strong U.K. in a strong European Union, which makes critical contributions to peace, prosperity, and security in Europe and around the world," White House spokesman Jay Carney said.

In contrast, Cameron's comments promised weaker EU links but denied Britain was headed for isolation.

Cameron argues his plans to take back some of the powers ceded to Europe can be part of a renegotiation process and promised to work toward an "in-out" referendum by 2017.

Cameron's comments met with derision from European officials and were seen as an embarrassing setback for Cameron. German Chancellor Angela Merkel sought to cool tempers, promising to talk with Britain over a "compromise."

BBC commentator Mark Mardell said Cameron's comments had caused "alarm bells" in the United States.

"The White House doesn't care about the EU's internal organization, and Europe is hardly its biggest concern anyway, but Mr. Cameron's promise (of a referendum) is definitely an unwanted irritation."

Mardell said, "In the modern version of the special relationship, what Carney called the essential relationship, Britain is valued as an ally precisely because it is one of the leaders of the biggest economy in the world," the European Union.

"The Americans are worried for several reasons. They fear the debate that will rage for the next few years will undermine Britain's voice in the EU and diminish its power.

"Indeed, insiders say that has already happened -- they find other EU members aren't taking Britain seriously," Mardell said.

Cameron's promise of an in-out referendum has spread uncertainty in British business and threatens its much delayed economic recovery from the 2008-09 downturn, The Guardian said.