SINGAPORE—North Korea said Wednesday that President Donald Trump had told Kim Jong Un that he intended to halt U.S.-South Korea military exercises and lift sanctions against the North, suggesting through its state media that Mr. Trump had explicitly acceded to two longstanding North Korean demands during bilateral talks at their summit meeting a day earlier.

The report put a distinctly North Korean spin on the summit meeting between the two leaders, the first between a sitting U.S. president and a leader of North Korea. The...