"The Economic Freedom Fighters has learned that the ANC is mobilising hooligans in the townships of Cape Town to come and assault EFF MPs today in Parliament," party spokesman Mbuyiseni Ndlozi said.
"The EFF has learned that they are loud-hailing across the townships, promising people free buses to go to Parliament and deal with the EFF."
Ndlozi said this was a "clear plan" to disrupt Parliament and render its work dysfunctional.
"It means the ANC is planning to undermine the very Parliament that it claims to protect and respect."
Moloto Mothapo, spokesman for ANC chief whip Stone Sizani, rubbished the claim and said the EFF had lost its mind.
"It's becoming clearer and clearer everyday that they are losing it. They are obviously imagining things, and this is a figment of their imagination," he told Sapa.
"Probably it is some sort of propaganda gone wrong on their part. They really have to come with something better if they want to be taken seriously. We have got no time to waste on the EFF."
A war of words between the EFF and the security cluster of ministers heated up on Tuesday following a meeting over the chaos in Parliament last week.
The justice, crime prevention, and security cluster condemned the action of EFF MPs who disrupted proceedings in the National Assembly last week while President Jacob Zuma was answering questions. Police were called in to calm the situation.
The cluster, led by Defence Minister Nosiviwe Mapisa-Nqakula, said extra-ordinary measures had been put in place to prevent a repeat of the incident.
Last Thursday, EFF leader Julius Malema was not happy with how Zuma had answered questions on when he would pay back part of the money spent on R246 million security upgrades to his private Nkandla residence in KwaZulu-Natal.
Speaker Baleka Mbete instructed Malema and his fellow MPs to leave the House when they kept interrupting and asking that Zuma answer their question.
Public Protector Thuli Madonsela had recommended in her report on Nkandla that Zuma repay that part of the money not spent on security measures, like the swimming pool and cattle kraal, among others.
Zuma has been accused of delaying his response in Parliament to Madonsela's report after he said he would leave it to Police Minister Nathi Nhleko to determine if he should repay any of the money.
On Tuesday night, Ndlozi said the security cluster had no business interfering in Parliament's processes because it was part of the executive.
"The doctrine of the separation of powers enshrined in our constitutional democracy prescribes that the executive, which is all appointed by the president, must respect Parliament," he said in a statement.
Parliament was capable of running its business, and there was never a need for the police to be called or for security measures to be tightened.
"The EFF will not be intimidated by a group of employees and henchmen/women who serve at the pleasure and discretion of President Zuma," said Ndlozi.
"The EFF is proud and makes no apology whatsoever for its peaceful protest action in Parliament last Thursday.
He said EFF MPs had the right to be in the Chamber and hold the executive accountable without any fear or favour.
Ndlozi said the EFF was ready for the ANC.
"If the ANC security cluster wants to arrest us, teargas us, or shoot to kill us, then let it be.
"The EFF is ready for any form of violence because no amount of war talk, no amount of intimidation will deter it from robustly raising issues and holding the executive accountable."