For most countries that received President Trump’s letters last week threatening steep tariffs, especially the Asian nations with economies focused on supplying the United States, there are no obvious substitutes as a destination for their goods.

But they are doing their best to find them.

Business and political leaders around the world have been roundly baffled by the White House’s imposition of new duties, even as governments shuttled envoys back and forth to Washington offering new purchases and pledges of reform. Mr. Trump is erecting new trade barriers and demanding deep concessions by Aug. 1, claiming years of grievance because America buys more than it sells.

“Across the world, tools once used to generate growth are now wielded to pressure, isolate and contain,” Anwar Ibrahim, the prime minister of Malaysia, said at a gathering of Southeast Asian leaders on Wednesday. “As we navigate external pressures, we need to fortify our foundations. Trade among ourselves. Invest more in one another.”

There are already a few signs of such efforts. South Korea’s new president, Lee Jae Myung, sent special envoys to Australia and Germany to discuss defense and trade issues, and plans on dispatching delegations to several others. Brazil and India announced plans to increase their bilateral trade by 70 percent, to $20 billion.

Indonesia says it is nearing a treaty with the European Union that would drop most tariffs on both sides to zero. And in Vietnam, which Mr. Trump said had accepted 20 percent tariffs on its goods headed to the United States before last week’s letters, the deputy trade minister emphasized efforts to reduce her country’s reliance on American consumers by leveraging other trade agreements.

“As more and more countries are feeling that it’s more difficult to satisfy U.S. demands, then their interest in working with others is going to intensify,” said Wendy Cutler, vice president at the Asia Society Policy Institute.

There is plenty of precedent for countries to seek other partners when their longstanding relationships sour.

During Mr. Trump’s first term, China retaliated against U.S. tariffs by buying smaller amounts U.S. soybeans. Brazil filled the hole and now supplies most of China’s soybean demand, leaving American farmers with too much product and not enough buyers.

In 2017, China boycotted goods from South Korea in retaliation for its willingness to host an American antiballistic missile system, seriously damaging South Korea’s China-dependent consumer and tourism industries. In response, South Korea expanded trade and investment with Indonesia, Malaysia and Vietnam.

Since Asian nations had already been working to diversify their customer bases, the current drive is not entirely new. But the region is still far from seamlessly integrated. South Korea, for example, has resisted joining the Comprehensive and Progressive Agreement for Trans-Pacific Partnership, a trade pact that rose from the ashes of negotiations with the United States that foundered in 2016.

Byung-il Choi, a South Korean economist and former trade negotiator, has been urging his country to join that agreement, which its neighbor Japan has signed. New hostility from Washington may finally make it possible, and South Korea’s president, Mr. Lee, has been more amenable to Japan than many expected during his campaign.

“Japan and Korea believed that we are a staunch, ironclad ally of the U.S., but Donald Trump doesn’t believe in allies,” Mr. Choi said. “So Japan is anxious to get more significant members, and Korea’s incoming government is saying, ‘In the name of national interest, we could do anything.’”

The latest tariff barrage has arrived as China has also been flooding the world with cheap goods to sustain its export-based growth. That oversupply of cars, appliances, electronics and textiles makes it harder for China’s neighbors to find their own niches.

Some of them could benefit from the Trump administration’s determination to prevent Chinese goods from filtering through other countries to American ports. Chinese businesses have already been setting up factories in Southeast Asia in search of lower labor costs, and the new agreements may encourage them to locate more of their supply chain outside China as well. Companies in the region, squeezed by competition from China and now by tariffs, could work to improve their productivity and maintain market share.

“They can do more efficiencies, maybe investing in new technology, digitalizing some of their factories, in order to reduce costs,” said Dionisius Narjoko, a senior economist at the Economic Research Institute for ASEAN and East Asia. “It could be cheaper to export, and therefore they can become more competitive in new markets or even in the U.S.”

To increase their citizens’ incomes, developing nations in Southeast Asia still need to create more homegrown enterprises. It’s not enough to remain the workshop for major powers. That requires steady leadership and focused investment, of the sort that allowed South Korea and Japan to grow into manufacturing powerhouses.

For example, while mostly Japanese companies now produce more than a million cars a year in Thailand, and the South Korean giant Samsung makes many of its cellphones in Vietnam, those Southeast Asian countries remain relatively poor.

“They need to internalize some industrial technology from the foreign direct investment,” said Kim Dongsoo, a senior research fellow with the Korea Institute for Industrial Economics and Trade. “Everybody knows that’s kind of a problem, but not all governments can escape from that trap.”

Ultimately, it could be advantageous for the countries that have become the targets of Mr. Trump’s tariff campaign to come up with a more collective response. So far, that hasn’t happened, as world leaders have continued to try to secure more favorable treatment for their own countries. Even the growing BRICS alliance, which drew Mr. Trump’s ire as it met in Rio de Janeiro and welcomed Indonesia as an official member, stopped short of taking any action to resist U.S. tariffs.

“I haven’t seen indications that Southeast Asian nations are trying to join together and present a united front,” said Alexander Hynd, an assistant professor at the University of Melbourne’s Asia Institute. But that could change if the current pace of upheaval continues.

“The U.S. is fairly rapidly attempting to dismantle the system that it set up, which is surprising a lot of people,” Mr. Hynd said.

Reporting was contributed by Choe Sang-Hun from Seoul; Ana Swanson from Washington; Alexandra Stevenson from Jakarta, Indonesia; and Tung Ngo from Hanoi, Vietnam.