Liefeld, who departed DC Comics amid a firestorm of controversy last week, published a direct messaging argument between the two on the microblogging site before the row continued publicly.
The former Deathstroke writer/artist referred to Snyder as a "pretentious prick" following a heated conversation in which the Batman writer claimed that the comic's success is down to him and artist Greg Capullo.
"Been berated in [direct messages] by Scott Snyder this morning. Excuse me if I don't marvel at your amazing abilities to write Batman. Piss off," wrote Liefeld.
"I'd like to think that if your going to wave your ego around on Batman you'd remember all that came before you. Holeee crap (sic)."
Snyder hit back at Liefeld, telling him that his Twitter feed is the best thing he has written all year. "I'll give you credit, Rob. Batman might sell in spite of me and Greg Capullo as you say, but Deathstroke and Hawkman failed because of you."
The row broke out after Snyder contacted Liefeld via direct message to establish whether critical comments he posted on Twitter in the wake of his DC departure were directed towards him.