The Al-Jamah-ah party has slammed the Department of State Security for not detecting a perceived "Satanic" desecration of about 80 graves at the Mowbray Muslim Cemetery in Cape Town.
"It is evil," said party leader Ganief Hendricks.
Earlier this week, tombstones at the cemetery were ripped out of the ground and arranged in the shape of a cross and other shapes.
Most of the tombstones affected were at the top end of the cemetery, next to Groote Schuur hospital.
Cemetery workers have put back most of them after appealing for help to identify which graves they belonged to.
Hendricks believed that Christians would never do such a thing. So, if it was not a Halloween prank, he was convinced Satanists were behind it.
Cemetery workers also discovered that some of the tombstones taken from other graves were arranged in a triangle inside freshly dug graves that are regularly prepared for burials.
Muslims have to be buried as soon as possible after death.
Hendricks said the graves were very deep, so a ladder would have been required to arrange the tombstones in a triangle shape inside them.
"It must have been quite an exercise. It must have been a massive operation," he said, questioning how nobody could have seen anything.
"The triangle is symbolism used by Satanists to express their cult," he said.
"It was to give expression to their Satanistic beliefs," he added.
Hendricks also said that there the perpetrators dug at seven graves, but no human remains were missing.
"I will ask the minister of intelligence (state security) why they are so slack. Why couldn't they pick this up?
"We are very concerned about all cemeteries in Cape Town now."
He said Satanists must realise that they are now a "legitimate target" in the police's investigation, but at the same time, called on Muslims to exercise restraint over the issue.
In the meantime, relatives have come to check whether graves of loved ones were affected, and almost all have been identified.
The cemetery workers helped restore the graves, and prayers were said afterwards.
Police said they were investigating a case of malicious damage to property.
Earlier this week, the Muslim Judicial Council's cemetery management committee head, Sheikh Riad Fataar, said families had to relive the trauma of burying loved ones as recently as a week ago.
"Some are saying it's Satanism, some are saying it has to do with Halloween. I am sending an e-mail this morning to the University of Cape Town's religion department to figure out what these symbols mean.