If the United States and China have succeeded at one thing this year, it is finding each other’s pain points.

An initial clash over tariffs has grown in recent months into a competition over which country can weaponize its control over the other’s supply chains.

China has clamped down on global shipments of rare minerals that are essential to building cars, missiles and a host of electronic products. The United States has in turn paused shipments to China of chemicals, machinery and technology including software and components to produce nuclear power, airplanes and semiconductors. As the conflict has escalated in recent weeks, it has caused Ford Motor and other companies to suspend some of their operations.

Both countries are now trying to find a way to defuse the situation. Top-ranking officials from the two sides are meeting on Tuesday for a second day of trade negotiations at Lancaster House in London, a historical site that has long been a stage for international treaties. They gathered just days after President Trump held a 90-minute phone call with Xi Jinping, the Chinese leader — the first time the two heads of state had spoken directly since Mr. Trump returned to office in January.

The haste with which the negotiations were arranged reflects the severity of the measures that both countries have recently adopted. After Mr. Trump ratcheted up tariffs on China to a minimum of 145 percent in April, Beijing clamped down on exports of critical minerals and magnets, threatening to shut down operations by American manufacturers, defense contractors and others.

U.S. and Chinese officials struck a temporary truce in a meeting in Geneva last month to roll back tariffs and, Trump administration officials believed, to restart a steady flow of rare earths to American companies. But shipments of the minerals, and the magnets made with them, remain infrequent and tightly controlled. In late May, Ford temporarily closed a factory in Chicago that makes its Explorer sport utility vehicle because of a lack of magnets.