Speaking during the debate on the presidency budget vote, Malema warned that Ramaphosa was following in his predecessor Jacob Zuma's footsteps in disregarding the remedial action of the Public Protector.
"We are going to use this Parliament to put pressure on you and on your friends, who are coming from the cabal, to respect the chapter nine institutions. I don't care who occupies that office, that office must be respected," Malema said.
"If honourable Pravin respected you and respected the new dawn, he will do what the deputy president did and say let me step aside until my name is cleared."
Malema was referring to two reports by the public protector which found Gordhan had acted illegally when he was SA Revenue Service commissioner - both of which are being challenged in court.
The EFF made headlines last week when its MPs were ejected after disrupting Gordhan's budget debate - in an attempt to stop him from speaking, calling him a "constitutional delinquent".
The actions of the EFF were largely criticised as other opposition parties accused the party of thuggery and several civil society organisations released statements in support of Gordhan.
Malema said this would not deter them. Instead, he signalled that the disruptions to the National Assembly which characterised the last few years of Zuma's presidency would be revived.
"We warned president Zuma repeatedly. I wanted to enjoy Parliament, I wanted to enjoy your presidency. You have got the best chance ever to lead us out of a nightmare of disrespecting institutions of this state. When you get such an opportunity you mess it up by protecting an individual..."