WASHINGTON—President Trump said Thursday the U.S. would impose escalating tariffs on all Mexican imports beginning June 10, in an effort to push the country to deter the flow of asylum-seeking Central American families to the southern border.

Reacting to what he described as “Mexico’s passive cooperation in allowing this mass incursion,” the president said the tariff on America’s third-largest trading partner would begin at 5% and grow steadily, hitting 25% on Oct. 1 unless Mexico takes satisfactory action to halt the migrants.

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