The president may want better deals to replace the old, “terrible” deals he doesn’t like, but so far, the rest of the world has been reluctant to negotiate new agreements with the United States. The long and growing list of tariffs, particularly those based on dubious national security grounds, has weakened the administration’s ability to form coalitions with other countries to tackle legitimate concerns, especially China’s unfair trade practices.

Instead, our closest trading partners are scrambling to find new markets for exports subject to tariff increases by the United States, and to secure new suppliers for the American products that their own countries are planning to hit with retaliatory tariffs.

Prime Minister Shinzo Abe of Japan, for example, has worked diligently to build close ties with the president. But now Japan’s top exports, autos and auto parts, are suddenly facing the threat of a 25 percent tariff. As Mr. Abe told Japanese legislators: “It’s hard for Japan to understand, and we cannot accept it.”

Japan is thus accelerating negotiations with other countries. Japan and the European Union plan to sign their free-trade agreement in July. Moreover, it was Japan who stepped up to fill the leadership void left by the American exit from the Trans-Pacific Partnership. The Japanese Diet approved a bill to ratify the revised pact this month.

The tone and policies of the Trump administration have even managed to bring two longtime rivals, China and Mexico, closer together. The two countries once competed head-to-head as low-cost manufacturers, with the United States as the most important market. After Mr. Trump began beating the drum for tariffs and a possible withdrawal from Nafta, Mexico’s economy minister, Ildefonso Guajardo, called a visit last year to China “strategic leverage,” saying it “sends the signal that we have alternatives” to the United States.

China, meanwhile, is on a mission to woo trading partners. Beijing’s campaign to be viewed as a champion of free trade and guardian of the multilateral trading system has been met with considerable skepticism. But efforts by China to promote stronger commercial ties with Japan, India and other countries are making headway. After a meeting in May with China’s premier, Li Keqiang, Mr. Abe said he wanted to “lift up the Japan-China relationship to a new stage.”

Regrettably, this leaves the United States on the margins as the rest of the world builds a new trading structure without us. Our workers, farmers and companies will be locked out of important markets. We will lose our chance to help write the rules and set standards for trade in advanced technology, such as alternative-fuel vehicles, 3-D printing and artificial intelligence. Global and regional supply chains will increasingly bypass the United States. And years of efforts by the United States to curb China’s unfair trade practices will lose critical international support.

To be sure, as the world’s largest economy, the United States will remain a major player in international commerce. Our market is a magnet for imports and our export competitiveness in manufacturing, services and agriculture is strong. The dollar remains the primary global reserve currency, with much of the world’s commerce denominated in dollars.

There is a danger, however, in overestimating our negotiating leverage. Trade patterns will shift as our partners look elsewhere. We have spent decades building trust with our allies. We are now squandering it.