Japan's main stock index, the Nikkei 225, gained 1.1 percent while the Shanghai Composite Index added 0.5 percent. Hong Kong's Hang Seng also rose 0.5 percent.
The conflict between the world's two biggest economies reflects chronic tension in their relationship as customers, business partners and increasingly as competitors. It also is rooted in the clash between American notions of free trade and Beijing's state-led development model.
China's ruling Communist Party has insisted on making changes at its own pace while sticking to state-directed technology development seen as the path to prosperity and global influence. Beijing has announced reforms this year including ending limits on foreign ownership in its auto industry, but none directly addresses complaints that are fueling its conflict with Washington.
On Thursday, Trump said higher tariffs on an additional $16 billion in Chinese goods were set to take effect in two weeks.
After that, the hostilities could intensify: Trump said Washington is ready to target an additional $200 billion in Chinese imports — and then $300 billion more — if Beijing does not yield.
That would bring the total of targeted Chinese goods to $550 billion — more than the $506 billion in goods that China shipped to the United States last year.
Chinese officials reject accusations they steal or force foreign companies to hand over technology. But rules on auto manufacturing and other industries do require companies to work through state-owned partners, obliging them to share know-how with potential competitors.
Other governments express similar complaints toward Beijing, but Washington has alienated potential allies by raising import duties on steel, aluminum and autos from Europe, Canada, Mexico and Japan. Some have responded by hiking their own tariffs on U.S. goods.
The official China Daily newspaper accused the Trump administration of "behaving like a gang of hoodlums." It said they would damage the global economy unless other countries stop them.
"There should be no doubting Beijing's resolve," the newspaper said.
Forecasters say global economic growth could be reduced by up to 0.5 percentage points in 2019-20 if both sides wind up raising tariffs on $250 billion of imports.
The American Chamber of Commerce in China appealed to both sides to negotiate.
"There are no winners in a trade war," the chamber's chairman, William Zarit, said in a statement. Companies want fairer treatment but will be hurt by U.S.-Chinese tensions, Zarit said. "We urge the two governments to come back to the negotiation table."