"They just made a very large order in the United States - and we appreciate that - for many billions of dollars, which means jobs for the United States and great, great equipment for Vietnam," Trump said.

Speaking at a dinner for the U.S. Chamber of Commerce Tuesday night, Phuc said the new deals would be concentrated largely in the high-tech sector. Even as Vietnam exports products like fish, seafood, apparel and footwear to the United States, it is a hungry consumer of U.S. corn, soybeans, planes and machinery, he said.

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But the newly announced deals may be little comfort for Vietnam after the collapse of the Trans-Pacific Partnership, the 12-country trade deal that Trump officially withdrew from shortly after he entered office.

Economists say Vietnam would have been one of the biggest winners of the deal. A 2016 study by the Peterson Institute of International Economics found that the Obama-era trade deal would have increased Vietnam’s gross domestic product by 8.1 percent by 2030, the most of any country in the deal, and expanded its exports by nearly a third. Economists expected the deal to expand access to foreign markets for Vietnamese producers of apparel, footwear and seafood, as well as stimulate economic reforms within the country.

In comparison, the TPP would have boosted U.S. GDP 0.5 percent and Japanese GDP 2.5 percent by 2030, Peterson estimated. Even countries with smaller economies, like Brunei and Peru, would not see as large of a percentage increase as Vietnam would have, according to Peterson's estimates.

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The deal also had strategic implications for Vietnam, a country of 90 million nestled against China's southern border. By excluding China, at least initially, the makers of the TPP sought to strengthen rival economies and balance China's increasing dominance of East Asia.

The visit also comes at a time when Trump appears to be warming to China, Vietnam's much larger and more powerful neighbor.

Looking to counterbalance China's economic and political influence in the region, the Obama administration had also sought to strengthen security ties with Vietnam, a strategic warming for two countries knit together by war that killed nearly 60,000 Americans and perhaps 3 million Vietnamese. The United States lifted a ban on arms sales and started joint naval drills in the South China Sea, the body of water off the coast of Vietnam in which China, the Philippines, Vietnam and other countries have rival territorial claims.

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While Trump frequently threatened China with hefty tariffs on the campaign trail, his rhetoric on China has softened considerably since coming into office.

The president backed down on his campaign promise to label China a currency manipulator — a charge which many economists had agreed was erroneous — saying that he had done so to gain China’s cooperation on North Korea. Trump also forged a 100-day action plan on trade with China that included several concessions, like allowing U.S. beef producers to sell into China and authorizing some financial companies to provide services there.

Robert Manning, a senior fellow at the Atlantic Council, said that the U.S. has two main concerns when it comes to trade with Vietnam: its growing trade deficit with the country and security cooperation in the South China Sea. For Vietnam, "Hanoi views the U.S. strategically as a counterbalance to China, on which it fears overdependence both economically and on security," Manning said.

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Trump's perceived warming toward China may worry leaders in Vietnam, which has also come under fire from the Trump administration for its economic practices. Like many countries, Vietnam exports more to the United States than it imports, creating a trade deficit that Trump has often railed against.

In 2016, the United States racked up a $32 billion trade deficit in goods with Vietnam, its sixth-largest. In late March, the president signed an executive order asking the Commerce Department to investigate the causes of trade deficits, with a focus on Vietnam and 15 other countries that had a significant trade deficit in goods with the United States last year.