Singer/songwriter Bugg, 18, told a reporter for Britain's Shortlist magazine he was stunned the What Makes You Beautiful hitmakers had been compared to the Beatles because of their U.S. success.
He added, "People (call them the new Beatles) because they broke America, but that don't mean a thing. I mean, (One Direction) must know that they're terrible. Calling them the new rock stars is a ridiculous statement. And people should stop making it."
Horan has hit back at Bugg in a post on his Twitter.com page, writing, "Really buggs (sic) me (is) that artists we're fans of, flip on us in the press!"
His bandmate Tomlinson added in a message to the singer, "Hi Jake Bugg do you think s**gging off boybands makes you more indie?"