Det Insp Viki Lanceley, of Merseyside Police, said the force was continuing to “update and support James’s family”.
“I would encourage anyone with information to come forward directly to police as soon as possible,” she said.
Katie McCreath, who is part of Denise Fergus’ legal team, said: “We are deeply saddened and angered to confirm that the headstone of James Bulger has once again been subjected to vandalism.
“This marks the second incident of its kind, and it is both distressing and unacceptable.
“Denise is understandably devastated.”