Joel, 61, and John, 63, toured extensively and performed concerts together for more than a decade.
"At the end of the day, he's coasting," John told Rolling Stone magazine last week. "I always say, 'Billy, can't you write another song?' It's either fear or laziness. It upsets me. Billy's a conundrum. We've had so many canceled tours because of illnesses and various other things, alcoholism."
The British star also compared Joel's efforts to stop drinking to his own battle with substance abuse.
"He's going to hate me for this, but every time he goes to rehab they've been light," John told the magazine. "When I went to rehab, I had to clean the floors. He goes to rehab where they have TVs. I love you, Billy, and this is tough love. Billy, you have your demons and you're not going to get rid of them at rehab light. You've got to be serious. People adore you, they love you and respect you. You should be able to do something better than what you're doing now."
Joel addressed John's remarks in a statement issued to E! News Friday. In it, he insisted:
"1. I do not hate Elton John.
2. I do not want to 'punch him in the face.'
3. If he wants to call me, my number is still the same.
4. Good luck with the movie."
The animated movie "Gnomeo and Juliet," which opens this weekend, features music John wrote and performed.
Celebrity Families of 2014 [PHOTOS]