By Mick Krever, CNN

Tensions between China and Japan, at their worst in half a century, are making conflict “much more likely now than it’s probably been in years,” the former top U.S. State Department official for East Asia told CNN’s Christiane Amanpour.

If a conflict were to break out, Kurt Campbell said, it would likely be a “small skirmish, probably easily contained.”

But the larger context, of "what is really the two great countries of Asia, China and Japan" is hard to ignore.

"Tensions between the two countries are greater now than they've been probably in a half century."

The two countries have long been loggerheads over uninhabited islands in the East China Sea – the Chinese call them Diaoyu and the Japanese call them Senkaku.

The heat was turned up, however, when China declared an “Air Defense Identification Zone” over the chain of islands.

The U.S. military responded by sending two unarmed B-52 bombers through the heart of the contested airspace.

America must make clear to China, Campbell said, that the drawing of a military air zone “is deeply provocative.”

“This is a recipe for the kind of incident that we saw in 1983,” he said, when the Soviet Union shot down Korean Air Lines Flight 007.

The U.S. has refused to recognize China air defense zone, but has nonetheless advised civilian aircraft flying through the area to notify the Chinese government.

That advice made the Japanese, with whom the U.S. has a military defense treaty, none too happy.

The U.S., Campbell said, has “two imperatives” – one military, and one civilian.

On the military side, he said, the U.S. was very clear that it would not acknowledge China’s new declared air defense zone.

But “civilian airspace monitors,” he said, “have a different set of metrics, and their prime directive is to avoid a mishap in the air.”

“Their initial guidance was apolitical in that sense,” he said. “But I think the problem is that it has created a little bit of incoherence.”

Campbell told Amanpour that he expected that Vice President Joe Biden to clarify the U.S. position. He met with Japanese Prime Minister Shinzo Abe on Tuesday and was set to talk with the Chinese leadership later in the week.

The U.S. military will continue to operate in China’s declared zone, Campbell said, as it long had.

But he added that he thought there would be “some clarifications” to the guidance from the U.S. Federal Aviation Administration “in the coming days or weeks that will make clear that we do not recognize this zone, but certain kinds of communication protocols will be followed to avoid a problem.”

“It’s imperfect, but given where we are that is the best we can do.”

In a larger sense, Campbell said, Biden will have to convince China and Japan to cool their heels.

“This is the cockpit of the global economy,” he said. “They are fighting over a barren rock in a distant part of the Pacific. Now I know it represents larger, sort of nationalist identities and the like, but these problems have existed for decades.”

The key is to “recognize that both countries have much bigger stakes than struggling over the identity of an uninhabited island in the middle of nowhere.”