"That's nonsense," he said, according to ESPN. "(Beal is) supposed to say that, but I know deep down, he's not messing with me and Ky (Kyrie Irving). I think me and Ky are the best backcourt, young backcourt. That's all."
Waiters started 24 games in 2013-14 for the Cavaliers, who went 33-49, and averaged 15.9 points and 3.0 assists.
Irving, the Cavaliers point guard and a two-time All-Star, averaged 21.3 points, 6.2 assists and 3.7 rebounds.
Wizards point guard John Wall was informed of Waiters' comments on Tuesday, and had his own response.
"You gotta win a playoff game first before you can talk. You gotta be a starter first," said Wall, according to Abdullah Sharif of hoopdistrict.net.
Wall and Beal helped the Wizards reach the Eastern Conference semifinals last season. Wall was named an All-Star and averaged 19.3 points, 8.8 assists and 4.1 rebounds. He tied for second-most assists per game in the NBA.
After being named to the NBA All-Rookie First Team in 2013, Beal averaged 17.1 points and 3.7 rebounds in 2013-14.
Cleveland had a busy offseason, signing LeBron James, James Jones and Shawn Marion and trading for the Timberwolves' Kevin Love.
- Molly Geary