The Economic Freedon Fighters (EFF) and Democratic Alliance (DA) have made separate calls for Zuma to be removed ahead of his state of the nation address (Sona) next week.
In separate letters to national assembly speaker Baleka Mbete, the opposition parties called for an urgent motion of no confidence debate and vote to be scheduled ahead of the Sona on February 8, or that the event be postponed.
EFF leader Julius Malema, in his letter dated January 30, said the party "emphatically requests" that Parliament schedule a motion of no confidence before Zuma takes the podium.
"This is largely informed by the fact that there are serious political developments and court judgments that necessitate an urgent parliamentary sitting to entertain a motion of no confidence against [Zuma]...The EFF is of a firm belief that Parliament will reasonably reach a different conclusion than in any of the previous sound [sic] attempts to rescue South Africa from an individual," he said.
"The suitability of [Zuma] to continue in the office of president is more of an urgent question now than a Sona to be delivered by an incumbent who is on the verge of commissions and trials. [Zuma] should not be allowed to deliver the Sona prior to a decision on whether parliament still has confidence in him to continue as a president," Malema added.
DA leader Mmusi Maimane wrote to Mbete on Wednesday, asking that the Sona be postponed until Zuma has been removed from office and Parliament is afforded the opportunity to elect a new president.
"As things stand, it would not be in the best interests of South Africa for [Zuma] to deliver the [Sona], when there exists great uncertainty as to whether he will remain [president], and if so, for how long," Maimane said.
"If [Zuma] does, in fact, deliver the Sona, this would further dent our already damaged credibility in the international community, as there would be no credibility to the programme of the state he would announce due to this uncertainty and ambiguity surrounding Zuma's future."
In a response to both letters, Parliament said on Wednesday that it would consider the requests and respond accordingly.