WBO super middleweight titleholder Saunders slammed Williams. "You big useless fraggle, that poor man clearly can't hold his hands up proper," he wrote. "When I'm in US, I'll move you around we see what happens then."
WBA and IBF super-lightweight champion Josh Taylor wrote: "Ammo Williams you're (a) liberty taking bully."
Rio Olympian and 12-1 professional Anthony Fowler added: "Bad s***house he is, bullying that."
But Williams didn't take the criticism well, calling out Saunders for a video of his own where he made jokes about how best to punch your partner during coronavirus lockdown.
"So Billy Joe Saunders is calling me out because I went a little too hard in sparring. And I'm only four years in the sport. But ain't this the same man who is suspended from boxing because he makes jokes about beating women? The woman-beater got something to say because I went a little hard in sparring, fresh off quarantine," Williams said.
"I want to see you. Let me know when you make it in the United States… I'm not scared of you," he added, before posting the address of his gym.
But he showed more contrition in a separate video.
"Just like everybody else, I'm sure this quarantine has played an effect on me," Williams said. "The quarantine cancelled my fight one week before it, so maybe I've got a little pent-up aggression, maybe I went a little too hard.
"I look back on the video and I see how it may be frowned upon because of how one-sided it was. I was not trying to embarrass my sparring partner, I respect any man that go into the ring.
"If you're watching this I respect you for getting in the ring, my intentions were not to embarrass you, my intentions were to show what I've been working on and it backfired."