North Korean leader Kim Jong Un at a military parade in Pyongyang, North Korea. (Wong Maye-E/Associated Press)

THE UNITED States and China appear to have reached a dead end on the growing problem of North Korean nuclear weapons. Both nations, in their own ways, lack a workable strategy for blunting Kim Jong Un, North Korea’s flamboyant leader, and his drive to perfect the nuclear bomb, which he has tested four times now. A meeting of Secretary of State John F. Kerry and Chinese Foreign Minister Wang Yi this week in Beijing revealed an impasse between Washington and Beijing even on how to respond to the regime’s latest nuclear test.

For China, the detonation on Jan. 6 was another in a series of pokes in the eye. North Korea defied pressure from Beijing not to act and did not even extend the courtesy of advance warning, as in previous tests. Yet despite its irritation, the government of Xi Jinping has evidently made a calculation not to squeeze North Korea too hard, lest it destabilize the regime, leading to what China fears most — the chaos of refugees from a collapsing state and a reunited Korea that would be a U.S. ally.

Mr. Wang assured Mr. Kerry that China would support a new resolution in the U.N. Security Council reproaching North Korea for the test. But he strongly suggested a resolution should not contain tough new measures to punish the regime — steps that China uniquely has the capacity to take because of its status as North Korea’s principal supplier of energy and other vital imports.

Mr. Kerry, for his part, has been lobbying China to shift its policy and use its leverage, and he radiated frustration after the lengthy meeting. “China,” he told reporters, “has a particular ability because of its special role and its connections to North Korea . . . to help us significantly to resolve this challenge.” He is right, of course. But it is becoming clear that the Obama administration’s policy of “strategic patience” toward the Kim regime — which in practice amounts to doing little other than weakly prodding China to act — is failing.

Mr. Kerry said that U.S. and Chinese officials would continue to work on a formula for a U.N. resolution. But the Obama administration needs a strategy for responding to North Korea that does not depend on China’s cooperation. It also needs to find ways to raise the cost for the Xi regime of its stubborn commitment to its neighbor’s “stability.”

There are steps the administration could take that would advance both aims. One would be to work with South Korea and Japan on the deployment of advanced missile defenses in those countries, something that would help protect them against the North Korean threat. China, which objects to a U.S.-South Korean missile deal, should be told it is a consequence of its own passivity. Congress should also act on proposals for unilateral U.S. sanctions that would target Chinese banks and companies that do business with North Korea — an approach that was effective with Iran.

Mr. Kerry said that the goal of U.S. policy is inducing North Korea to resume negotiations on giving up its nuclear arsenal. If that is to be achieved, the United States will have to do much more than hope that China will apply the necessary pressure.