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 report quoted Mr. Kim as saying that, if the U.S. were to take “genuine measures for building trust,” then the North could reciprocate in a “commensurate” fashion—a clear suggestion that U.S. concessions would have to come before any North Korean move.

While Mr. Trump had said during a press briefing after the event that he would halt joint military exercises while talks were ongoing with the North, Pyongyang’s report suggested that Mr. Trump had also given such a commitment directly to Mr. Kim, after the North Korean leader had called on Mr. Trump to halt “irritating and hostile military actions.” The joint statement signed by the two men a day earlier didn’t make mention of joint exercises, mentioning only unspecified U.S. “security guarantees” toward the North.

Mr. Trump also told reporters during his press briefing that he was planning to hold the line on sanctions against North Korea, saying the U.S. still had “tremendous pressure” to keep economic penalties in place—a contrast to Pyongyang’s portrayal of Mr. Trump telling Mr. Kim that he intended to end sanctions. The report didn’t mention any timeline for lifting the sanctions.

The North Korean report quoted Mr. Trump as crediting Mr. Kim’s “proactive peace-loving measures” for having created the atmosphere of peace this year—not the president’s “maximum pressure” campaign against Pyongyang—and said the two leaders accepted each other’s invitations to visit their respective countries.