The official results from national elections last month just don’t add up for Mbalenhle Mthethwa, a loyal adherent of a new political party led by Jacob Zuma, South Africa’s former president.

“The elections were not free and fair,” she said, echoing the stolen-election narrative advanced by Mr. Zuma. Ms. Mthethwa, a 38-year-old chef, lives in a township near the coastal city of Durban and has been out of work for the past four years.

Mr. Zuma, 82, whose nine years as president were marred by allegations of corruption and looting of state coffers, has taken a page from the playbook of populist leaders of recent years — notably in the United States and Brazil.

Vote-rigging claims in other nations have resulted in chaos, and South Africans will get a first look at how things might unfold on Friday, with Mr. Zuma’s party, uMkhonto weSizwe, known as M.K., vowing to boycott the first sitting of the newly elected Parliament.

The boycott would not prevent Parliament from accomplishing its goal that day — electing a president and a speaker. But it would provide a high-profile stage for the party to express its anger.

Mr. Zuma’s party actually outperformed the expectations of analysts and political rivals: It won nearly 15 percent of the vote nationally, making it the third-largest party in Parliament, and 45 percent in Mr. Zuma’s home province, KwaZulu-Natal.

Still, Mr. Zuma and his supporters claim they won at least two-thirds of the vote, enough to change the nation’s Constitution to pursue some of their proposed initiatives, although they have not presented evidence. Those initiatives would include allowing traditional ethnic leaders to have a role in Parliament and paving the way for Mr. Zuma — who is ineligible to serve because of a criminal conviction for refusing to testify before a corruption inquiry — to return as president.

Beyond Parliament, Mr. Zuma’s supporters have said they would remain disciplined and would await instructions from him on how to respond to what they see as a system stacked against them.

The latest fodder for their grievance came on Wednesday evening, when a terse, four-page decision by the nation’s top court threw out M.K.’s application to prevent the opening of the parliamentary session.

The party had argued that the new Parliament should not be allowed to meet because the election results were in doubt. But the court said the party waited too long to file its application and that it had not presented sufficient evidence to support its case.

M.K.’s electoral showing was unprecedented for any South African party competing for the first time in national and provincial elections in the post-apartheid era. And it was a big reason that Mr. Zuma’s former party, the African National Congress, lost its absolute majority for the first time since coming to power at the end of apartheid in 1994, though it still captured more votes than any other party.

The A.N.C. has invited all political parties to join an alliance to govern the country, and the parties were still negotiating on Thursday with a deadline to strike a deal before Friday’s parliamentary session.

M.K., named after the armed wing of the A.N.C. during the fight against apartheid, has rebuffed the A.N.C. Mr. Zuma’s party says it would not entertain a partnership with the A.N.C. under President Cyril Ramaphosa, his former deputy with whom he had a bitter falling out after being forced to resign as president in 2018.

The extent to which M.K. has upended the A.N.C. is most evident in KwaZulu-Natal communities including Ms. Mthethwa’s township, KwaMakhutha, a hilly, hardscrabble outpost just down the street from a touristy beach town.

Five years ago, the A.N.C. won Ms. Mthethwa’s ward with 76 percent of the vote. This year, M.K. won it with 75 percent. The M.K. branch in the area has about 5,000 members, said Ms. Mthethwa, who is the coordinator for the branch, and most of them have defected from the A.N.C.

Ms. Mthethwa said she was not politically active and was not really a fan of Mr. Zuma until she heard his message at the launch of M.K. in December. Her community suffers from high unemployment, shortages of water, electricity outages and cratered roads, a reflection of a country that is in a desperate situation.

“There are certain people, when they talk, they command your attention,” she said, adding that she believed Mr. Zuma when he said “this is the party that’s going to save all people who are living in South Africa.”

What resonates most in communities like KwaMakhutha is M.K.’s message to fight for the nation’s Black majority, which still faces deep disparities in wealth, land ownership and other economic measures three decades after the end of apartheid. Ms. Mthethwa said the best way for the party to endear itself to the community was to essentially be good neighbors.

On Wednesday, at an old animal pharmaceutical shop with an exposed cinder block wall in KwaMakhutha, several M.K. volunteers folded clothes they had collected to donate to community members whose homes were destroyed in flooding last week. Up the road, several young men who now back Mr. Zuma’s party sat next to an open lot where they were planning to plant a vegetable garden for the community after having cleared it.

“The vision of the M.K. party is to bring back the dignity of the Black people,” said Sthobela Khuzwayo, 21, who embraced the new party even though he is from a family of A.N.C. activists.

Having worked as a monitor at the polls on Election Day, Mr. Khuzwayo, too, believes that his party was robbed. The party is still trying to find ways to challenge the official outcome, but if it is unable to do so, he said, it would be prudent to take up its 58 seats in the 400-member Parliament.

“You can’t produce any change,” he said, “without our members inside the Parliament.”