Trump attacked James on Twitter last Friday following an interview regarding his new school opening in Akron. The president said CNN's Don Lemon "made Lebron look smart, which isn’t easy to do."
Rodgers appreciated the fact that James hadn't responded to the latest attack, saying it was "absolutely beautiful."
"I think that the more that we give credence to stuff like that, the more it's gonna live on," he said. "I think if we can learn to ignore or not respond to stuff like that—if we can—it takes away the power of statements like that."
Trump has repeatedly gone after athletes since becoming president, most notably attacking NFL players who kneel during the national anthem during last season. He called for owners to fire Colin Kaepernick and anyone else who "disrespects our flag."
While Rodgers wasn't one of the players who joined in the protest against racial injustice, he did provide several supporting posts on his Instagram account, calling for "unity" and "equality for all."
The two-time MVP is heading into his 14th season in the NFL.