BEIJING. “We are probing, so stay tuned,” Secretary of State Rex W. Tillerson said, about how he might begin a conversation with Kim Jong-un, the North Korean leader. “We ask, ‘Would you like to talk?’ We have lines of communications to Pyongyang — we’re not in a dark situation, a blackout. We have a couple, three channels open to Pyongyang,” he added.

U.S. Secretary of State Rex Tillerson called Saturday for a calming of the situation on the Korean Peninsula, but said it was incumbent on North Korea to halt its missile launches.

Following meetings with Chinese President Xi Jinping and other officials in Beijing, Tillerson said he believes China has become deeply concerned about the North’s missile and nuclear programs and is working hard to convince Pyongyang to re-enter talks, but did not say specifically what form those talks should take.

“I think the most immediate action that we need is to calm things down,” Tillerson told reporters. “They’re a little overheated right now. And I think we need to calm them down first.”

Asked whether that should apply to recent pointed remarks from President Donald Trump, Tillerson replied: “I think the whole situation is a bit overheated right now. I think everyone would like for it to calm down.

“Obviously it would help if North Korea would stop firing off missiles. That would calm things down a lot,” Tillerson said.

Ties between Beijing and Washington are considered more crucial than ever with the standoff over Pyongyang’s nuclear weapons and ballistic missiles entering a new, more dangerous phase as its leader, Kim Jong Un, and Trump exchange personal insults and threats of war with no sign of a diplomatic solution.

Trump has been pressing for tougher measures on Pyongyang from China, the North’s chief trading partner and source of aid and diplomatic support. Although adamantly opposed to steps that could bring down Kim’s regime, Beijing appears increasingly willing to tighten the screws on Pyongyang, and agreed to tough new United Nations sanctions that would substantially cut foreign revenue for the isolated North.

Tillerson reiterated Saturday that the U.S. would not recognize North Korea as a nuclear power, but said it also had no intention of overthrowing Kim’s regime.

In opening remarks at his meeting with Xi, Tillerson said relations between the sides continue to “grow and mature on the strength of the relationship between yourself and President Trump.”

“And we look forward to advancing that relationship at the upcoming summit,” Tillerson said, referring to Trump’s first state visit to Beijing expected in November.

Saying he had “a good working relationship and personal friendship” with Trump, Xi said the president’s upcoming visit offered “an important opportunity for the further development of China-U.S. relations.” The exchange, he said, would be a “special, wonderful and successful one.”

Earlier, Tillerson told top Chinese foreign policy adviser Yang Jiechi that a strong relationship between Trump and Xi bode well for dealing with political and economic differences between the two countries.

“Our two presidents have developed a very regular and close working relationship,” Tillerson said.

Trump’s visit, Tillerson said, also provided an opportunity to assess progress made between the sides since Xi and Trump met in April at the U.S. president’s estate in Florida.

There they agreed to a 100-day plan for trade talks. After visiting China this week, U.S. Commerce Secretary Wilbur Ross said there’s been some progress, including a deal to let U.S. beef into China, but they need to tackle “bigger things and more difficult things.” The U.S. priorities are better market access, less protectionism and protecting intellectual property rights.

Tillerson is making his second visit as secretary of state to the world’s No. 2 economy and chief American rival for influence in Asia, and increasingly, the world. Along with Xi and Yang, he met with Foreign Minister Wang Yi, who told Tillerson that China-U.S. relations “overall have a positive momentum and have arrived at an important opportunity to progress further.”

On Thursday, Beijing ordered North Korean-owned businesses and ventures with Chinese partners to close by early January, days after it said it would cut off gas and limit shipments of refined petroleum products, effective Jan. 1. It made no mention of crude oil, which makes up the bulk of Chinese energy supplies to North Korea and is not covered by the U.N. sanctions.

China has also banned imports of North Korean coal, iron and lead ore, and seafood since early September.

Still, Washington hopes China will exert even greater pressure, even while Beijing says the impasse can’t be solved by sanctions alone and calls on Washington to cool its rhetoric and open dialogue with Pyongyang.

Other than North Korea, the U.S. and China have other security concerns to address. They remain at odds over Beijing’s military buildup and assertive claims to disputed islands in the South China Sea.

Tillerson is also expected to restate concerns about China’s massive trade surplus with the U.S. — $347 billion last year — and what American companies say are unfair barriers to investment, including pressure to hand over their technology.

Washington wants Beijing to make good on its promise to let market forces have a bigger role in its economy, give equal treatment to foreign and Chinese companies and roll back state industry’s dominance.

Trump’s planned visit to China in November will come just weeks after Xi is expected to receive a new five-year term as leader of the ruling Communist Party.

Despite his tough criticism of China’s trade practices, Trump has forged a personal connection with Xi over phone calls and while hosting him in Florida, during which they agreed on four high-level dialogues to cover various aspects of relations.

The November meeting of the two leaders will be grander and more choreographed than the informal talks in Florida that were most memorable for Trump’s ordering a missile strike on Syria and then informing Xi about it afterward as they ate chocolate cake.

Tillerson, facing criticism at home for his muted impact as the top U.S. diplomat, may also be seeking to put his own stamp on the relationship. He surprised some observers during his first official visit to China in March when he employed China’s own words to characterize relations between the sides — language the Obama administration had largely rejected as an attempt by Beijing to establish a type of moral parity between the sides.

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By CHRISTOPHER BODEEN

Associated Press writers Joe McDonald in Beijing and Mathew Pennington in Washington contributed to this story.