"I like to think Mr. Carter and I understand each other," Obama said. "Nobody who met us as younger men would have expected us to be where we are today. We know what it's like not to have a father around. We know what it's like not to come from much, to know people didn't get the same breaks that we did, so we try to pop up those doors of opportunity."
The 21-time Grammy winner made history by becoming the first rapper
to be inducted into the Songwriters Hall of Fame.
"Jay and I are also fools for our daughters," Obama continued, "although he's gonna have me beat once those two twins show up, and let's face it, we both have wives who are significantly more popular than we are."
Jay Z -- whose wife, Beyoncé, is in the advanced stages of her pregnancy, which has spurred speculation
from fans that she might have already delivered the twins -- did not personally appear at the ceremony, but his longtime music publisher and friend Jon Platt accepted the award on his behalf.
The rapper, who is not a frequent social media user, went on a tweetstorm to thank those who inspired him, including Obama, tweeting, "And the greatest rapper of all time OBAMA . Thank you 44."
Obama recalled how the rapper's music inspired him as President — the time he sampled Jay's lyrics in his March 2015 speech to commemorate
the 50th anniversary of "Bloody Sunday" in Selma; the time he "tweeted a reference to 'My First Song'
as I was putting the finishing touches on my final State of the Union address," and the time he "brushed the dirt off my shoulder during a campaign."
Obama discussed his favorite rappers, including Chance the Rapper and Kendrick Lamar, in an October 2016 interview
on SiriusXM's "Sway in the Morning," but declared that "Jay Z's still the king."
The 2017 class of inductees also includes R&B legend Kenneth "Babyface" Edmonds, Motown founder Berry Gordy, songwriting duo Jimmy Jam and Terry Lewis, pop music writer Max Martin and Chicago members Robert Lamm and James Pankow.