Motshekga, who is also a member of the party's constitutional committee, further said last week's special extended meeting of the ANC's national working committee (NWC) was "irregularly constituted".
The NWC meeting followed unprecedented public disagreements by party officials over Zuma's controversial Cabinet reshuffle, which saw the sacking of finance minister Pravin Gordhan, among others.
In an interview with News24, Motshekga said the NEC is the only "competent" body to have a final say on the matter of Zuma's recall. Motshekga is the first senior ANC member to publicly call for a special NEC.
"It was not adequate for the NWC, which was irregularly constituted, to have a final say on the matters raised by society. The correct position is that on matters of such importance, the NWC must make recommendations to the NEC or a properly constitutional constituted NWC," Motshekga said.
The NWC meeting held last Tuesday was extended to include only provincial chairpersons and secretaries.
Calls for Zuma to resign
The NWC discussed the intensified calls for Zuma to resign, coming from within the ANC, alliance partners Cosatu and the SACP, and the public discontent with the president.
At a media briefing following the meeting, ANC secretary general Gwede Mantashe said the provincial chairs and secretaries were called as per the party's constitution.
Mantashe said they were invited to speed up communication.
The ANC constitution states that the NWC, whose members are elected from the NEC to deal with the day-to-day running of the organisation, may "invite any ANC member in good standing to attend the meeting", but while the invitee may speak and participate for the purposes for which he or she was invited, they cannot vote.
Motshekga said inviting only the provincial chairs and secretaries "created suspicion" and has "never been done before".
"Usually an extended NWC meeting is extended to members of the NEC who can attend. You don't exclude them and invite provincial chairs and secretaries, that raises suspicion and one can read many things into that.
"The NEC is the only competent body to deal with the call for Zuma to resign because it is the highest decision making body between conference and existence of the NWC," Motshekga said.
Zuma supporters were confident ahead of the NWC meeting, saying they believed the inclusion of provincial leaders would bolster their numbers.
Deepening crisis 'unacceptable'
The renewed calls for Zuma to step down were spurred by his decision to reshuffle his Cabinet, firing five ministers including Gordhan. His decision has led to two ratings agencies downgrading South Africa to "junk status", and is expected to affect the inflation rate, leading to interest rates hikes.
The rand also lost more than 10% of its value since Gordhan was recalled from his investor roadshow, which is expected to lead to an increase in the price of petrol, which will have a domino effect on the price of food.
Tens of thousands of South Africans across the country took to the streets last Friday to call for Zuma to step down. Another march, this time by opposition parties, is due to be held in Pretoria on Wednesday.
Last November, now axed tourism minister Derek Hanekom led the charge at an NEC meeting for Zuma to step down following a massive decline at the polls during the local government elections.
The motion however failed after the "rough" discussions that continued for two days were extended by another day. Motshekga said the situation has since "worsened", and the marches calling for Zuma to go had put the matter back on the agenda as they are a "barometer necessary to engage the mood of the people".
Motshekga added he did not find anything wrong with the marches. He dismissed a question on Zuma supporters dominating the NEC, saying another meeting would likely have the same outcome as the November meeting.
"I think that members of the ANC are not children, I think all of them would find the deepening crisis unacceptable and realise that it is their responsibility to address the situation or go themselves," Motshekga said.
However he warned that for the NEC to resign, it would lead to a leadership vacuum.
"The ANC was elected to run the country, and it deployed one of its members as president. Now the people that elected the ANC into power are saying 'we are not happy with your deployee, your deployee must step down', and there are some within the ANC, within the alliance... who are saying the same thing.
"So if the ANC does not agree, it must meet and consider the grounds on which the demands are made - then [it must] go back to society and say we accept or reject and advance reasons, whichever decision they are taking," Motshekga said.
Last year, Motshekga penned a column saying the party's decision to accept the decision of the Constitutional Court, which found that Zuma had "violated the Constitution and oath of office, was accepted for political expediency" and the leadership "must convene an urgent NEC meeting and ask the president to do honourable thing".
He said the party now again had to convene the NEC meeting and "put the people of South Africa first and discuss the matter without fear or favour".
"So for me there is no crisis, because the NEC has not met. So most urgent intervention must come from NEC, it must be convened urgently, " Motshekga said.
He warned that the party's NEC should choose between Zuma and the ANC and the people of South Africa.
No regime change agenda
Motshekga dismissed criticism from Zuma that the marches were racist and claims by his supporters that the "people's march" last week was part of a regime change agenda.
"Their [civil society] demands are explicit, they are saying the president must go and they spell out reasons for saying so - that is different from regime change because regime change is about overthrowing the government.
"There is no element of that nature [regime change] here and is not a matter between the protesters and the president, it is a matter between the ruling party and the protesters."
Motshekga said the party must reconsider calls by stalwarts for a consultative conference. The ANC had decided that the first two days of the June policy conference must be set aside for the consultative conference, a decision rejected by the stalwarts, who want a separate conference.
Motshekga said the consultative conference would help the party to redeem its credibility ahead of the December elective conference and 2019 general elections. It would also ensure the policy conference has the "authority and weight" it deserves.
Motshekga said many people are "talking on behalf of the people but acting in our own interest, because it is a struggle for power which doesn't take people themselves anywhere".