The words “Doctrine of Hate” and “Architect of Genocide” were daubed in red on the grave of Highgate Cemetery’s most famous resident.
A marble plaque was also smashed up in the “senseless, stupid, ignorant” attack, said the charity which runs the cemetery.
The latest defacement comes after the monument, which attracts tens of thousands of visitors a year, was damaged with a hammer earlier this month.
Visitor Maxwell Blowfield said he was shocked to discover the vandalism on Saturday morning.
Mr Blowfield, 31, who works as a press officer with the British Museum, said: “It’s a highlight of the cemetery. It’s a shame. The red paint will disappear, I assume, but to see that kind of level of damage and to see it happen twice, it’s not good.
“I wouldn’t like to say who or why someone did it but it was clearly someone very critical of Marx and that part of history. I am just surprised that somebody in 2019 feels they need to and do something like that.”
A post on the cemetery’s Twitter account condemned the vandalism.
“Whatever you think about Marx’s legacy, this is not the way to make the point,” it added.
The Friends of Highgate Cemetery Trust said that Marx’s grave appeared to have been targeted in a “deliberate and sustained attack” following the first incident of vandalism on 4 February.
Ian Dungavell, the trust’s chief executive, described the damage as “very upsetting”.
The marble plaque on the tomb was first used on the grave of Marx’s wife, Jenny von Westphalen, in 1881. It was moved when the couple’s remains were exhumed and reinterred in a more prominent location in the cemetery in 1954.
In the 1970s, the memorial was damaged by two homemade bombs. It is Grade I-listed, putting it on a par with the most important buildings in the country.
The monument is owned by the Marx Grave Trust, which is represented by the Marx Memorial Library in Clerkenwell.
Police said no arrests have been made over either the 4 February vandalism or the most recent attack.
A Metropolitan Police spokesman said: “We would appeal to anyone who has any information to contact us.”