Liverpool said they saddened by the recent rise in "vile chants" about the Hillsborough Stadium disaster and that they will call on the "full force of the law" to stop it.
Ninety-six Liverpool supporters were crushed to death in an over-crowded and fenced-in enclosure at the Hillsborough Stadium in Sheffield before an FA Cup semi-final between Liverpool and Nottingham Forest in April 1989.
Another victim died last June, 32 years after suffering severe and irreversible brain damage.
Liverpool's statement came after Manchester United condemned fans who chanted "completely unacceptable" songs about the disaster during Tuesday's defeat by Liverpool at Anfield.
"Liverpool FC is saddened by the recent rise in vile chants about the Hillsborough disaster," Liverpool said in a statement on Thursday.
"We know the impact these abhorrent slurs have on the families of the 97, those who survived, and all associated with this club.
"We are working with the relevant authorities to do our utmost to ensure these chants are eradicated from football altogether and, where appropriate, bring the full force of the law and the game's sanction process down on those who continue to sing them."
Last weekend, Manchester City apologised after some fans disturbed a minute's silence marking the 33rd anniversary of the disaster during their FA Cup semi-final defeat by Liverpool at Wembley.