The party led by South Africa’s former President Jacob Zuma has asked the country’s highest court to stop the newly elected national assembly from sitting for the first time on Friday.
It is a key date because that is when members of parliament are due to vote for the country’s president.
But Mr Zuma’s uMkhonto weSizwe (MK) party is boycotting the session, claiming there were irregularities in last month’s general election – although it has not provided evidence to support this.
Mr Zuma, a former ANC leader, is an ally-turned-enemy of President Cyril Ramaphosa, who is seeking a second term.
Mr Ramaphosa is the leader of the African National Congress (ANC), which lost its parliamentary majority for the first time since it took power at the end of the racist system of apartheid in 1994.
The ANC won 40% of the vote, not enough to govern alone.
It is now involved in talks with other parties as it scrambles to form a government of national unity.
Mr Zuma blames Mr Ramaphosa for ousting him as president in 2018, when the party removed him partly because of corruption allegations
Last December, Mr Zuma announced that he would be campaigning for MK.
MK caused a major surprise by coming third in the election – the first it contested since registering as a party last September.
The unexpected strength of its showing cut into the ANC’s vote share, and is a factor behind the ruling party’s poor results.
MK also emerged as the biggest winner in Mr Zuma’s home province of KwaZulu-Natal, but failed to get an outright majority to gain control of the government there.
It is the only party to have demanded that Mr Ramaphosa step down.
The main opposition party, the Democratic Alliance (DA), has not confirmed it plans to vote for Mr Ramaphosa to be re-elected. But neither has the party said it would not back him.
“The focus on the negotiations now is finding solutions to the process towards formation of governments [at national and provincial level],” DA spokesman Solly Malatsi told the BBC.
“Ramaphosa is the president of the ANC and that’s the knowledge on which we are all negotiating with,” he added.
In legal papers submitted to the Constitutional Court, MK alleged that South Africa’s election commission was wrong to call the results of May’s general election free and fair.
It also argues that holding Friday’s parliamentary sitting would be unconstitutional, saying there would not be enough members present.
And the party is demanding that the president call another election within 90 days.
It is unclear whether this legal move will have any impact.
Parliamentary officials had previously dismissed the MK’s objections, saying its interpretation of the constitution was incorrect, and the chief justice went ahead with announcing a date for the first sitting.
The BBC News