BEIJING—China’s imports fell for a fourth straight month in August as a drop-off in exports to the U.S. steepened, the most recent economic warning signs during a prolonged trade spat with the U.S. that has Beijing turning toward stimulus measures.

Chinese imports of everything from raw materials to high-tech products dropped 5.6% in August compared with a year earlier, the same decline as July, the Chinese customs data showed. Although August’s drop was smaller than economists had expected, a downturn in demand highlights...