"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.
•SI's Top 100 NBA players of 2015
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