The mayor of Liverpool has said it is "despicable" that the word "invaders" has been written across a memorial to dead refugees and migrants.
It was daubed on The List, which displays the names of 34,361 asylum seekers, refugees and migrants who have died within or on the borders of Europe since 1993.
Joe Anderson said the offenders "had their brains invaded by hatred".
Merseyside Police said it had not received any reports of damage.
The installation on Great George Street is part of a festival of contemporary art running until October.
Liverpool Biennial, which commissioned the project, is yet to comment.
Designed by artist Banu Cennetoğlu, the memorial has been torn down twice this summer.
In August, she issued a joint statement with Liverpool Biennial saying the work had been "repeatedly damaged, removed and targeted since it was installed" on 12 July.
They said The List has not been attacked in any of the other places it has been installed, such as Berlin, Istanbul, Basel and Athens.