WASHINGTON — As he tries to tackle the greatest challenges to American power in Asia, President Trump is overturning policy toward China and North Korea that for decades was as canonical as Confucian ritual.

With North Korea, he is engaging with the enemy in hopes that negotiations will yield a surrender of nuclear weapons. With China, Mr. Trump says the United States must take a big step back from an economic relationship that has strengthened a formidable rival.

The shifts were prompted by internal changes in each country, combined with Mr. Trump’s unorthodox instincts and the views of his senior Asia advisers. The administration now has growing bipartisan support in Washington to widen an emerging global conflict with China and build diplomacy with North Korea.

This week, American negotiators are pressing forward with the policy transformations.

Treasury Secretary Steven T. Mnuchin and Robert E. Lighthizer, the United States trade representative, spoke to Chinese counterparts on Tuesday by telephone to continue tough trade negotiations. Meanwhile, Stephen E. Biegun, the special representative for North Korea, was in Brussels and Berlin to discuss diplomatic approaches to North Korea.