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.