This comes after the EFF threatened to take legal action over Mahumapelo’s decision to appoint finance MEC Wendy Nelson to act on his behalf while on leave.
EFF leader Julius Malema called Nelson’s appointment an illegal arrangement.
The EFF would lodge an urgent application to have it reversed, he said.
“You cannot do that. We are going to write to them (the North West government) a letter to tell them that if they don’t remove that, we are going to make an urgent application to court,” he said in Johannesburg on Thursday.
“You can only appoint a premier if the premier is out of the country or (when) the premier is absent or not in a position to exercise his powers. So the freedom is there for him to exercise his powers. He is around,” Malema said.
Following his earlier decision to resign on Tuesday night, Mahumapelo and the ANC provincial executive committee reversed his resignation and declared war on those who want him out.
On Thursday, Mahumapelo - who branded mounting calls for his removal from within the ANC-led alliance as an act of persecution by backers of President Cyril Ramaphosa - indicated that he was unfazed by those who wanted to challenge his appointment of Nelson while still keeping his post.
He told Independent Media he was not running the provincial administration as he was already on leave.
“Those who want to launch a court challenge must go to court. No problem,” Mahumapelo said.
A seemingly relaxed Mahumapelo however refused to discuss the actual legality of his leave of absence, saying Nelson would instead be the one to defend it.
“I am unable to comment on this decision now. The acting premier will respond to this and its legality."
Constitutional law expert and political analyst Professor Shadrack Gutto said Mahumapelo’s decision was illegal.
“Taking leave of absence must have specifics both in terms of how the person is absent and the length of time in which he will be absent. The decision he made was both irrational and illegal as he exercised power he does not have.
“Now we have two premiers in the province effectively. One is sitting at home drawing a salary while the other pretends to be in charge.
"This arrangement could be seen as aimed at minimising the pressure of the calls for him to step down while ensuring he remains in charge by choosing someone who will protect and do his bidding,” Gutto said.
North West ANC spokesperson Gerald Modise insisted Mahumapelo’s decision was legal and the ANC would support it, even if it were legally challenged.
“We took that decision as the PEC. It is in compliance with the constitution because it says when the premier is absent, he can appoint an acting person.
"The premier is absent from his position now. I don’t know where he is currently but he is absent and absent does not mean a person has to be out of the country."
On Wednesday a defiant Mahumapelo said that for the next 18 weeks he would be visiting the 18 sub-regions of the party in the province to tell branches the “truth” about attempts to oust him.
His defiant posture has put the current ANC national executive committee, the party’s highest decision-making body, under the spotlight, as it has the power to select and recall premiers in provinces governed by the ruling party.
The party in the province has however maintained that it was not defying its national structures as no upper structure has informed it of any decision to instruct Mahumapelo to step down.
Meanwhile, the Inter-Ministerial task team sent to the province will stay in the area for some time to fix the province.
This indication was given by Communications Minister Nomvula Mokonyane om Thursday following the cabinet meeting in Cape Town.
The findings on the state of affairs in the province of the task team, led by Minister in the Presidency Nkosazana Dlamini Zuma, have not been made public.
Mokonyane said the report would be released next week.
The cabinet was applying its mind to some of the report's recommendations.
Opposition parties have accused embattled Mahumapelo of running the province into the ground.
Mokonyane said the task team submitted its preliminary report to the cabinet, which discussed its findings but did not elaborate.
“We did receive the preliminary report on North West. We did reflect on the recommendations of the preliminary report."