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The tension surrounding North Korea, meanwhile, is sending a new jolt through the wider debate about nuclear proliferation in Asia. There were signs Wednesday that a new arms race is heating up in the region, with The Wall Street Journal reporting that South Korea is now pressing the Obama administration for permission to produce its own nuclear fuel.

Some foreign policy analysts note that the North Korea crisis may force the Obama administration, which has tended to address the varied nuclear ambitions and concerns of the region on a nation-by-nation basis, to rethink its approach to security in East Asia.

“The strategic and nuclear calculations of China, Korea and Japan are becoming more and more tightly connected,” said Henry D. Sokolski, who heads the Non-Proliferation Policy Education Center, a think tank based in Washington. “Every time you talk about one of these countries, you now have to be thinking hard about the other two.”

With Mr. Kerry and Mr. Hagel, along with Chairman of the Joint Chiefs of Staff Gen. Martin E. Dempsey preparing rare trips to Beijing later this month, the relationship has been complicated in recent years by China’s rise as a major global economic power.

North Korea is just one of many “issues on the agenda in the U.S-China relationship,” Mr. Snyder said. “So one of the challenges has been figuring out where this belongs as an issue on the agenda.”

In that, the Obama White House appears to have struggled badly. Specifically, recent years have found senior officials far less than eager to speak publicly about the administration’s true strategy for dealing with North Korea.

“The administration didn’t see much benefit in highlighting an issue where there’s very little space to take an initiative without risking potential for failure,” Mr. Snyder said. “I think one of the effects of the Obama administration’s downplaying the issue, was that it sent a message to the Chinese that the U.S. sees it as unimportant, when that was actually not the case.”

Most Western foreign policy analysts agree that China’s interests are rooted in a desire to grow its own regional power base — a policy that would, inherently, resist a Washington-engineered resolution to the Korean conflict.

During a meeting Tuesday with ambassadors from North and South Korea and the U.S., China’s foreign minister “expressed serious concern” about the recent wave of tension of the Korean Peninsula and urged all sides to “remain calm and exercise restraint,” according to a report by Reuters.

However, the remarks coincided with reports that Beijing continues to quietly build up its military assets in northeastern China, a move some believe is tied to the crisis with North Korea.

Such belief appears to have been on the mind of Mr. Hagel, who reached out by telephone Tuesday evening to his Chinese counterpart, Gen. Chang Wanquan.

During the call, Mr. Hagel “emphasized the growing threat to the U.S. and our allies posed by North Korea’s aggressive pursuit of nuclear weapons and ballistic missile programs,” the Pentagon said in a statement.

The defense secretary also “expressed to Gen. Chang the importance of sustained U.S.-China dialogue and cooperation on these issues,” the statement said.