West's social media pages show him in a red "Make America Great Again" hat, and he has said he wishes to facilitate conversations between the president and opponents like National Football League free agent Colin Kaepernick.
The rapper also ruled out a presidential bid "until 2024", instead voicing his support for Trump, saying he "loves" the president, before hugging him.
At one point, West stood up and reached across the table to show Trump a picture of a hydrogen-powered plane, which the rapper told the president ought to replace Air Force One.
West - best known as Kanye but recently stated that he wants to be known as Ye - is one of the mould-breaking president's more unusual supporters.
"He's said very nice things about me in the past ... extremely positive things", Trump said. He said the hat given to him by the president was like "a Superman cape".
This is the second time West and Trump have met.
They were joined by Jim Brown, the legendary former Cleveland Browns running back, as well as Ivanka Trump and Jared Kushner. Much of the time was spent on compliments between the two and West's much-talked about support for the president.
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"What I need SNL and liberals to improve on is, if he don't look good, we don't look good", he said on Thursday.
Earlier this week, Mr. Trump said there are a lot of people like Johnson and he would like to find them.
The politician and attorney continued, "Just the other day, [West] was talking about STEM programs and how we needed to have more STEM programs and had to turn around and ask his colleague, what did STEM mean?"
"And also, I'm married to a family that, you know - not a lot of male energy going on".
"That was quite something", Trump said at the end West freewheeling soliloquy. "I just channeled it", West responded. His wife, reality TV star Kim Kardashian West, has worked with the White House on criminal justice reform and clemency issues.
Seated across from Trump at the famous Resolute Desk, West began the Oval Office meeting - which also included NFL Hall of Famer Jim Brown and Trump's son-in-law and senior adviser Jared Kushner - with a almost 10-minute-long speech that the rapper said was "from the soul", according to White House pool reports.
"It hurts us because we need to focus on who were are today", he said.
"Oh! It's good energy in this", he said.