His comments marked the first sign that the Trump administration has been trying its own version of what the Obama administration did with Iran: using a series of backchannel, largely secret communications that, after years of negotiation, resulted in a nuclear accord.
But Mr. Tillerson was quick to distinguish the very different circumstances of North Korea and Iran — Pyongyang has nuclear weapons, Tehran just a program that could have led to them — and then added: “We are not going to put together a nuclear deal in North Korea that is as flimsy as the one in Iran.”
Speaking less than an hour after he left a meeting with President Xi Jinping of China, Mr. Tillerson said the most important thing was to lower the temperature of the threats being exchanged in recent days between Mr. Kim and President Trump.
“The whole situation is a bit overheated right now,” he said. “If North Korea would stop firing its missiles, that would calm things down a lot.”
When asked whether that caution applied as well to Mr. Trump, who tweeted last weekend that if the North were to keep issuing threats, “they won’t be around much longer,” he skirted any direct criticism of the president.
“I think everyone would like for it to calm down,” he said.
Although Mr. Trump has recently been exchanging insults and threats with Mr. Kim, the president said early in his campaign that he would be willing to sit down with the North Korean leader and perhaps have a hamburger with him.
That the United States would be in contact with North Korea is not surprising, said Narushige Michishita, director of the Security and International Studies Program at the National Graduate Institute for Policy Studies in Tokyo, “But it sounds a little too early.”
“The timing is unexpected,” he said. “It was perfectly clear that both North Korea and the United States, and others, are in the prenegotiation bargaining process.”
In Japan, where Prime Minister Shinzo Abe recently dissolved the lower house of parliament and called a snap election, the news that the United States is already in direct contact with North Korea could give ammunition to Mr. Abe’s opponents. The Japanese leader has steadfastly maintained that it is not the time for dialogue, arguing in a recent Op-Ed article in The New York Times that “emphasizing the importance of dialogue will not work with North Korea.”
“Now,” Mr. Michishita added, “the opposition party members can say ‘Look, you have been talking about pressure, but the U.S. is just leaving you behind.’ ”
Earlier in the day, Mr. Xi told Mr. Tillerson that he wanted to ensure the success of a planned visit to China by Mr. Trump in November, according to a summary of their meeting issued by the Chinese Ministry of Foreign Affairs. That summary did not mention any discussions about North Korea.
The Chinese foreign ministry did note that China’s foreign minister, Wang Yi, and state councilor, Yang Jiechi, who also oversees foreign policy, had discussed the North Korean crisis with Mr. Tillerson. But those accounts gave no details.
Mr. Yang told Mr. Tillerson that their two governments should “enhance communication and coordination over major international and regional issues,” according to the ministry.
Mr. Tillerson attended three back-to-back meetings in Beijing’s Great Hall of the People, just off Tiananmen Square, after his trip was delayed by a malfunction in his plane. The aging Boeing 757, which his predecessors all complained about, stranded him in Japan during a refueling stop.
He eventually reached Beijing, half a day late, after boarding a C-130 cargo plane, leading to the unusual sight of an American secretary of state walking off the rear ramp of an aircraft better known for shuttling tanks.
Mr. Tillerson then had just six hours or so to meet with Beijing’s leadership before most of China shut down for Golden Week, a holiday that starts with the national day. That will be followed by the Communist Party Congress, a meeting that occurs once in five years.
The congress represents Mr. Xi’s moment to solidify his reputation as one of the strongest Chinese leaders in decades. In the run-up to the Congress, Beijing has sought to preserve the status quo.
Mr. Tillerson and his Chinese interlocutors reflected that desire in their public comments, none of them mentioning the words “North Korea” as they made opening remarks. Instead, they talked, as if on cue, about Mr. Trump’s planned travels in November, which will include stops in China, Japan and South Korea.
But at the end of the day, settling into a couch at the residence of Ambassador Terry Branstad, a former governor of Iowa, Mr. Tillerson tried to sound optimistic that traditional diplomacy would help resolve the North Korean issue, even though it has failed past presidents.
He insisted that the ultimate goal of the negotiations would be complete denuclearization, a goal many experts believe is far out of reach. The North has made clear that its nuclear arsenal is a pillar of the state, a position acknowledged in its constitution.
“They can change their constitution,” Mr. Tillerson said. “Especially the people running North Korea — it’s pretty easy for them to change it.”
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