BEIJING — As a presidential candidate, Donald J. Trump talked about China almost solely in the context of trade, such as when he promised to slap punishing tariffs on cheap Chinese imports that he argued had ruined the lives of working-class Americans.

But as he begins to feel the weight of office on his shoulders, there are signs that his focus in the Asia region may have shifted toward security — specifically, the problem of North Korea and its expanding nuclear arsenal, which experts say already threatens America’s regional allies, Japan and South Korea.

During his visit to The New York Times this week, Mr. Trump referred obliquely to a “big problem for the country” that President Obama had mentioned during their 90-minute meeting at the White House after the election. Well-placed American officials believe that reference was to North Korea.

Any solution to that problem must involve China, North Korea’s patron, American and Chinese officials agree. Mr. Trump acknowledged as much during the campaign, saying on one occasion that China should do more to bear down on the North.

So which tack will Mr. Trump take with China? Will he seek its support for a deal on North Korea, or will he start a trade war, putting such cooperation in doubt?

American officials briefed the Chinese several months ago on their assessment that the North’s nuclear capabilities had sharply increased, according to two Americans with knowledge of the briefings, who spoke on the condition of anonymity because of the sensitivity of the matter.

But even before then, nuclear scientists from China and the United States had agreed for some time about the danger posed by the North’s ambitions, said Siegfried S. Hecker, an American nuclear scientist at Stanford University who was the last outsider to visit the country’s plutonium processing plant at Yongbyon, in November 2010.

Several years ago, the Chinese tended to play down the North’s nuclear capabilities, Dr. Hecker said in an email exchange. But since the mercurial Kim Jong-un, a young leader who has declined to listen to China and has provoked the United States, took over the country, the assessments of the two powers have been “pretty much in line,” he said.

Dr. Hecker and other scientists estimate that North Korea might develop the capacity to strike the West Coast of the United States with a nuclear warhead in about five years. But the real problem is here and now, in Asia, he said.

“The greatest and most urgent threat comes not from a North Korean nuke being able to reach the U.S., but rather what they have already,” he said. Specifically, Dr. Hecker wrote in a recent article, the North is now probably able “to put nuclear weapons on target anywhere in South Korea and Japan and even on some U.S. assets in the Pacific.”

Worse yet, he wrote, North Korea may have developed a “false sense of confidence” from a recent spate of successful nuclear and missile tests — one that could lead it to grave errors of judgment.

By the end of this year, Dr. Hecker estimated, the country is likely to have enough fissile material for about 20 bombs. The danger would be exacerbated if the North decided “to field tactical nuclear weapons as its arsenal expands and its confidence in its nuclear arsenal grows.”

In short, Dr. Hecker said, more and better bombs make a catastrophic miscalculation by North Korea more likely.

How much of this Mr. Trump knew before his victory is unclear, but he was certainly aware of the problem. Early on, he expressed a mixture of awe and dismay toward Mr. Kim.

“If you look at North Korea, this guy, I mean, he’s like a maniac, O.K.?” he said at a rally in Ottumwa, Iowa, in January.

“And you’ve got to give him credit. How many young guys — he was like 26 or 25 when his father died — can take over these tough generals?” Mr. Trump was referring to Mr. Kim’s execution of several generals, including his uncle, Jang Song-thaek, who was the main conduit between North Korea and China.

“We can’t play games with him,” Mr. Trump said at the time, referring to Mr. Kim. “Because he really does have missiles, and he really does have nukes.”

Such considerations — and briefings that Mr. Trump presumably has received or will receive on the North’s capabilities — could compel the new president to prioritize security over trade in his dealings with China. With the right approach, he could find a willing partner in Beijing, said Yang Xiyu, a former Chinese official who oversaw the so-called six-party talks on the North’s nuclear program that collapsed in 2008.

But Chinese officials say that approach would require removing a thorn in Beijing’s side: an advanced missile defense system that the United States plans to install in South Korea. The Chinese view that system, known as the Terminal High Altitude Area Defense System, as an effort to contain its ambitions in Asia, though Washington and Seoul say it is intended purely to defend South Korea against the North.

In the past year, China has rebuffed many of Washington’s requests for sharper measures against North Korea, and the missile system is one reason. Whether Mr. Trump would consider scrapping it is another unknown.

Washington and Beijing did cooperate on United Nations sanctions against the North this year — an encouraging sign, analysts said, though many doubt that economic punishment alone will be a deterrent.

And on Friday, the Chinese state-run news media reported that Beijing would support a new round of sanctions being considered by the Security Council that would close loopholes allowing North Korea to sell coal.