"This is serious. We must deal with this issue," said Nxesi, who was previously the minister of public works, and survived Zuma's Cabinet reshuffle last week.
He was speaking at the party's Cape Metro chapter meeting at the Cape Peninsula University of Technology.
After some ribbing from SACP members teasing the party's portly national deputy chairperson over his sporting prowess, Nxesi said the latest political developments were an urgent call for the mass democratic movement to mobilise.
He said there was at present a lack of people who are as humble and willing to make sacrifices as the late ANC veteran Ahmed Kathrada, which made it easy for people with money to get elected.
"As we move into the national conference of the movement, money talks, people are buying branches," he said, slamming state capture and corruption.
'Petty and spiteful' fighting
Commenting on allegations of a plot by former finance minister Pravin Gordhan to remove Zuma, he said: "We cannot believe that he could go out and mobilise the whole world against the country that we fought for".
He was also shocked by the "petty and spiteful" fighting over whether Zuma should have attended Kathrada's funeral and memorial services, or not.
"How do we do that to a man of the calibre of Comrade Kathy?" he asked.
He read the statement issued by the SACP politburo on Friday, in which Zuma was called "reckless" and was asked to step down, and told delegates that it was up to them whether he and other SACP-aligned ministers should stay put, as the politburo said, or whether they should step down.
The party is in an alliance with the African National Congress and the Congress of SA Trade Unions, but has been considering whether to go it alone and contest elections itself.
Many of the delegates were familiar faces from strikes by unions aligned to the Congress of SA Trade Unions, including the protracted National Education Health and Allied Workers Union strike at Parliament in 2016.