WASHINGTON—The Trump administration said Tuesday it would extend $12 billion in emergency aid to farmers amid signs the U.S. agricultural sector is beginning to feel the impact of President Donald Trump’s escalating trade disputes with major U.S. trading partners.

Agriculture Secretary Sonny Perdue said the U.S. government would provide incremental payments to support prices of some of the hardest-hit commodities, including soybeans, sorghum, cotton, corn, wheat and pork.

“This...