This is not the first time that a secretary of state has sought to play the missile defense card. Mr. Tillerson’s immediate predecessor in the job, John Kerry, told the Chinese that if China succeeded in constraining Pyongyang’s military ambitions, the United States could limit and perhaps even withdraw some of its antimissile systems in the region.

“The president of the United States deployed some additional missile defense capacity precisely because of the threat of North Korea,” Mr. Kerry said after an April 2013 visit to Beijing. “And it is logical that if the threat of North Korea disappears because the peninsula denuclearizes, then obviously that threat no longer mandates that kind of posture.”

But there is no evidence that China, perhaps fearing instability on the Korean Peninsula, ever applied the sort of pressure that would have prompted North Korea to shelve its military programs.

It is not clear how explicitly Mr. Tillerson, a diplomatic novice with no past experience in proliferation issues, will deliver the message to the Chinese at a moment that he will also be trying to set up the first meeting between President Trump and President Xi Jinping, at the Mar-a-Lago resort in Florida early next month.

During the presidential campaign, Mr. Trump said he was willing to sit down with North Korea’s leader, Kim Jong-un, and negotiate with him directly, perhaps over a hamburger. Since then, Mr. Trump has taken an increasingly hard line, and suggested that he would link China’s use of its influence over the North to other issues, including trade relations.

Last week, the Chinese repeated a proposal they knew the United States would reject, calling for a freeze in North Korea’s nuclear and missile programs in return for a cessation of American and South Korean annual military exercises, which are just now beginning. The Trump administration immediately rejected that call, saying that it would reward the North if it complied with United Nations resolutions it had long ignored, and would make the United States’ defense arrangements with South Korea a subject of bargaining.

Reinforcing military ties, Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, conducted a 30-minute phone call on Tuesday with his South Korean counterpart, Gen. Lee Sun-jin. A Pentagon statement said the generals discussed the possibility that North Korea could carry out “provocative actions” during the joint American and South Korean exercises now underway, or in April when North Korean authorities commemorate the birthday of Kim Il-sung, the founder and first leader of the country.