"You are trying a good wine," West said, praising himself. "He has complex notes for it."
At one point, Mr. West pulled out his iPhone to show the president some illustrations of a hydrogen-powered plane that he said could replace Air Force One.
"Look at this, Jared," Mr. West told the son-in-law and chief adviser to the president, Jared Kushner, as he presented him with drawings of his idea, the iPlane 1.
"We will get rid of Air Force One," the president replied. "Can we get rid of Air Force One?"
Meanwhile, Mr. Trump sat with his hands together on the resolute desk, nodding as the musician continued. When Mr. West referred to the plight of a 68-year-old prisoner who planned to argue with the president, Mr. Trump did not seem to recognize the man's name when it was mentioned.
"Actually, the reason he was jailed is because he started being positive for the community, he started to show that he really had power," West said. "Then, there are theories that there are infinite amounts of the universe, and there is an alternative universe."
After Mr. West's speech ended, Mr. Trump stayed momentarily and strangely, without words, while the advisors, including Mr. Kushner and Ivanka Trump, watched. Mrs. Trump showed a wide smile, while Mr. Kushner pressed his hands against the handles of his chair.
"I tell you what," said Mr. Trump. "That was pretty impressive."
Mr. West agreed.
"It was from the soul," said the musician. "I just channeled it."
Seated near Mr. West was Jim Brown, the former Cleveland Browns runner. Mr. Brown, who has supported the president in the past, hardly received a word.