The giant sculpture was attacked in June and then cleaned, but Kapoor said that this time the graffitti would remain on the work, to bear witness to hatred.
Officially known as "Dirty Corner," the sculpture comprises a huge steel funnel that the 61-year-old British-Indian artist has described as "very sexual."
It and the rocks around it were sprayed in white paint with phrases such as "SS blood sacrifice," "Queen sacrificed, twice insulted," "the second RAPE of the nation by DEVIANT JEWISH activism" and "Christ is king in Versailles," the palace management said.
Culture Minister Fleur Pellerin said the vandalism was an "attack on freedom of creation" and the phrases were "unacceptable."
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The steel-and-rock sculpture, which faces the royal chateau, is 60 metres long and 10 metres high.
Shortly after the sculpture was unveiled in June, vandals splattered it with yellow paint.
"I had already questioned the wisdom of cleaning it after the first vandalism. This time, I am convinced that nothing should be removed from these slurs, from these words which belong to anti-Semitism that we'd rather forget," Kapoor said in comments Le Figaro published in French.
"From now on, in the name of our universal principles, these abominable words will become part of my work, they will overlay it and stigmatise it."
"We have some ideas about those who fit the profile," the source added.
For his part, Kapoor said he was struck by the spirit behind the vandalism and its "connection with the terrible situation between Syria and Europe.
"This is what leads to the exclusion of our Syrian brothers and sisters. Shame on France for the act of a hate-filled minority! This is a violent attack against the human spirit and culture."
The sculpture is one of several by Kapoor which are on show in the gardens and inside one room of the palace until November.