Spotify AB removed from its music service in the U.S. thousands of songs by bands signed to independent record label Victory Records amid a standoff over publishing royalties, the two companies said on Monday.

The dispute centers on publishing royalties that Victory’s sister company, Another Victory Music Publishing, says it is owed by the subscription music-streaming service. Based on an audit by a small technology company called Audiam Inc., Another Victory says that Spotify hasn’t paid publishing royalties for the compositions...