For his part, Mr. West dodged questions about the possibility of performing at Mr. Trump’s inauguration in January. The rapper only smiled at reporters and said, “I just want to take a picture right now.”

It is unclear why the musician and sometime fashion designer stepped out from a reported recovery and into the center of the media circus at Trump Tower, but Hope Hicks, Mr. Trump’s spokeswoman, said in an email that Mr. West had requested the meeting.

“The meeting was requested by Kanye and we were delighted to host him,” Ms. Hicks wrote, adding, “They had a very positive and productive conversation.” She did not elaborate, but later in the afternoon, Mr. West said on Twitter that he wanted to meet with Mr. Trump to discuss “multicultural issues” that included “bullying, supporting teachers, modernizing curriculums and violence in Chicago.”

He added: “I feel it is important to have a direct line of communication with our future President if we truly want change.”