>>>STATE DEPARTMENT -- U.S. Secretary of State John Kerry and United Nations Secretary-General Ban Ki-moon say North Korea's nuclear test this week must not go unpunished.

As crowds in Pyongyang celebrate what North Korean leaders call a successful nuclear test in legitimate self-defense, U.N. Secretary General Ban Ki-moon says the test is a direct challenge to the international community.

"I have repeatedly called on the leadership of Pyongyang to give up its pursuit of nuclear programs and to instead focus on building a better future for the country's people by addressing dire humanitarian and human rights situations," Ban said.

Ahead of talks with Ban, Kerry said North Korea is a clear threat to world peace.

"This week's test was an enormously provocative act that warrants a strong, a swift, and a credible response from the global community," Kerry said.

North Korea's third nuclear test in defiance of a U.N. resolution drew widespread criticism, including from China, which is Pyongyang's only major ally.

Kerry says China could do more to discourage North Korea's nuclear program.

But Cato Institute analyst Justin Logan says Washington has given Beijing little incentive to take a harder line against Pyongyang.

"The Chinese know that they are sort of in the cat-bird seat when it comes to North Korea.  But I think there's been not much willingness shown by Washington to do very ambitious things vis-a-vis Korea to trade off in other areas," Logan said.

For example, reducing U.S. military support for South Korea as Logan says China has longstanding concerns about what a reunified Korean peninsula would mean for its own security.

"They look down the road and say if our policies today produce in 10 years or 15 years a unified Korea with American military troops on our border, that's a problem," Logan said.

While the nuclear test further isolates North Korea, Renmin University professor Shi Yinhong says there are limits to how far China will go to help.

He says China will not support extremely wide and strict United Nations financial sanctions against North Korea because that would heavily impact Chinese trade.  So while China will keep discussing it with the United States, Bejing will not support all of those demands.

John Hopkins University professor Ruth Wedgwood says it is wrong to think China has anything to gain by helping with North Korea.

"Personally, I have always entertained the alternative hypothesis: that they kind of like having North Korea as a stick to goad us with, stick it in our eye, realize that it would be an irritation," Wedgwood said.

She says China is far more interested in expanding its reach than in reigning in North Korea.

"I think China is playing its own game here.  They have never been helpful with us on North Korea.  They are again feeling that they have a chance to be quite dominant in the region," she said.

Secretary Kerry and Secretary-General Ban say they are working with U.N. Security Council members and other allies to guarantee an appropriate response to the nuclear test.

North Korea is threatening stronger steps if necessary to counter what it says is U.S. hostility toward the communist state.