"Those in the music business say he's a genius, and that's okay with me".
West continued: "Let's stop worrying about the future, all we have is today".
West's visit follows two visits by his wife Kim Kardashian West, who has met with Trump at the White House and successfully secured a presidential pardon for a woman who was serving a life sentence in prison over non-violent drug charges.
In an interview with Fox News before the meeting, Trump said the justice system was "very unfair to African-Americans it's very unfair to everybody. He might not have thought he'd have a insane motherf**ker like (me)". West dined on roasted chicken and fingerling potatoes over lunch with Trump, Jared Kushner and Ivanka, fellow musician Kid Rock and Hall of Fame running back Jim Brown.
Ahead of a private lunch, Mr Trump and West spoke with reporters as they sat across from each other at the Resolute desk.
Adidas CEO Kasper Rorstedtold CNBC earlier this week that West has been a "fantastic ambassador" for the company, though he admitted he was unaware that the rapper meant to meet with Trump for lunch.
"It's harder to govern", Melania Trump said in a clip that aired Thursday on "Good Morning America".
It nearly sounded as if reforming the prison system was a top priority for President Trump since it is "very costly" and challenged his own Attorney General, Jeff Sessions.
National Football League legend Jim Brown also attended the meeting.
At the end of the weirdest Oval Office meeting ever, Kanye gave Trump a hug.
He showed the president a video on his phone of a plane powered by hydrogen, and suggested that Mr. Trump should fly in it.
Trump said he is willing to "look at it", and said "they have to do something". "I love everyone, but the campaign "I'm with her" just didn't make me feel - as a guy".
West also mentioned North Korea and said, to Trump, "You stopped the war". "So, there's theories that there's infinite amounts of universe, and there's alternate universe".
F-35 Jets: Military grounds entire fleet
The Air Force has 156, the Marine Corps has 61 and the Navy has 28, according to data provided by the joint program office. More than 320 F-35s around the world must now undergo the inspections, according to a source familiar with the program.