The EFF wants to test the resolve of ANC members of the North West legislature to get rid of embattled Premier Supra Mahumapelo.
The party is abandoning its court challenge for a secret ballot in the motion of no confidence against him.
Instead, it will now write a letter to the speaker of the legislature to demand that the motion be debated urgently.
"We have no sympathy for Supra. Secret ballot or no secret ballot. We want to expose the crooks inside the ANC, to see if they mean business when they say they want Supra to go. Why don't they vote with the EFF in our motion of no confidence?" EFF leader Julius Malema said.
He was speaking in Coligny, North West, at a rally to celebrate the party's Ward 15 victory in by-elections last month.
The speaker of the legislature had earlier decided to indefinitely postpone the EFF's initial motion of no confidence, when it approached the court to demand a secret ballot.
'No need for bloodshed'
Malema accused some members of the legislature, including those from the SACP, of refusing to use their powers within the legislature to rid the province of Mahumapelo.
"When we gave them a tool to remove Supra without a drop of blood, through a motion of no confidence, they refused," Malema said.
The ANC's national working committee (NWC) was due to meet on Wednesday to discuss Mahumapelo's fate. Members of the NWC have argued however that only the national executive committee (NEC) has powers to recall a premier.
A battle is expected when the NEC sits this month to discuss the matter, among others.
"We don't want a drop of blood. We want you to take government using your votes [instead of violence]," Malema said.
"A motion of no confidence is a peaceful thing introduced in our Constitution by Mandela and [others]. They are refusing to use it," he said.
Protests not 'genuine'
Malema labelled Mahumapelo as corrupt, accusing him of stealing money from various government departments meant for the poor.
He denounced the violence that recently gripped the North West. Several towns ground to a halt as residents looted shops and set alight public buildings, demanding that Mahumapelo step down.
A 16-year-old boy was killed during the unrest.
Malema warned EFF members against participating in the protests, which he said were part of factional battles within the ANC.
"I don't want the red berets in places being burnt. Don't get involved in the looting of shops, it is an ANC thing to do. They are fighting factional battles, it's not a genuine fight. If it was genuine why don't they use the EFF's motion of no confidence to remove Supra without a drop of blood?" he asked.
Malema said the EFF would remove Mahumapelo the same way it removed former president Jacob Zuma, who was now sitting idle in his home village of Nkandla.
The EFF exerted pressure on the ANC NEC to remove Zuma by calling a motion of no confidence against him in Parliament.