WASHINGTON — President Trump’s trade war with China entered new territory on Sunday as his next round of tariffs took effect, changing the rules of trade in ways that have no recent historic precedent and driving the world’s two largest economies further apart.

American tariffs on foreign goods had already climbed higher than any time since the 1960s before Sunday, when the United States imposed a new 15 percent tariff. The levies on food, clothing, lawn mowers and thousands of other “Made in China” products come as the president prepares to tax nearly everything China ships to America. The move will bring average tariffs on Chinese imports to 21.2 percent, up from only 3.1 percent when Mr. Trump came into office, according to data from the Peterson Institute for International Economics.

China has responded by raising barriers to American companies and their products, while easing them for other nations. Trade between the world’s two largest economies has slumped, and China, which had long been America’s biggest trading partner, dropped to third place in the first half of the year, behind Mexico and Canada.

American companies that once believed the trade war would blow over are now scrambling to limit their exposure to China, in some cases shifting production to other countries, like Vietnam, to avoid tariffs that will soon reach as much as 30 percent.