The DA has accelerated calls for Parliament's dissolution, an idea which some of its opposition partners have rejected.
The party tabled a motion on Thursday, to be voted on at the earliest opportunity. It claimed the ANC no longer enjoyed the support of the majority of South Africans, and early elections must be held.
On Wednesday, DA leader Mmusi Maimane called for the dissolution of Parliament. This followed Tuesday's failed motion of no confidence in President Jacob Zuma via secret ballot.
UDM leader Bantu Holomisa said his party did not support the DA's proposal for dissolving Parliament, but respected its right to propose the motion.
"Of immediate importance to the UDM is the state of readiness of the IEC for the 2019 general elections," Holomisa told News24 on Thursday.
The Electoral Commission of SA (IEC) had to move with speed to ensure the voter's roll was up-to-date and had voters' addresses, in line with a previous Constitutional Court ruling, he said.
He called on the ANC to ensure the IEC got the R300m budget it needed to hold the elections in 2019.
'Don't strengthen Zuma's faction'
FF Plus leader Pieter Groenewald said the DA's motion was opportunistic and would not succeed.
"Every time Zuma survives a motion it strengthens his supporters within the ANC, as it creates the impression that he is a strong leader who is untouchable."
Groenewald said voters were getting despondent that Zuma kept surviving, and might lose interest in the 2019 general elections.
EFF leader Julius Malema taunted DA members on Twitter, suggesting they could dissolve Parliament if all their MPs resigned. This was not accurate, as only a passed motion could dissolve Parliament.
"U don't need a motion @Our_DA, you can do it alone (sic). If @EFFSouthAfrica had more than 51 members, we were gonna do it alone. Stop bluffing," he tweeted.
- Read more: Can Parliament dissolve if enough MPs resign?
The EFF on Thursday said in a statement it would not entertain the DA's motion because it was disingenuous.
Spokesperson Mbuyiseni Ndlozi said they approached the DA with the same proposal after the Constitutional Court's Nkandla judgment of March 31, 2016. The court found President Jacob Zuma violated the Constitution when he ignored former public protector Thuli Madonsela's recommendation that he repay some of the R246 million spent on so-called security upgrades to his private homestead.
The court found Parliament had failed to hold Zuma accountable.
"This judgment implied that the 5th democratic Parliament is illegitimate. On this basis the EFF approached the DA that Parliament must be dissolved through Section 46, and the DA refused," Ndlozi said.
IFP Chief Whip Narend Singh said the DA's call came as a surprise and they had not discussed it yet.
Singh said it was unlikely his party would just agree simply because the DA had called for it. It required a lot of consideration, also money, and should not be taken lightly.
'Country in need of fresh mandate'
DA deputy chief whip Mike Waters said South Africans should be given the chance to state if they still had faith in the ANC.
"According to the Constitution, after three years you're entitled to dissolve Parliament if the need arises, and we obviously believe the need has arisen."
He said during the motion of no confidence debate, the ANC said it was confident voters still supported the party.
"I don't see why they would be scared to go to the country and get a fresh mandate."
Waters said the country had changed over the last three years since the fifth Parliament was elected in May 2014.
"It's proven without a shadow of a doubt that the government is corrupt, has been captured, and that within the ANC there are now divisions. So therefore a fresh mandate needs to be sought from the electorate."
Waters said he could not comment on Holomisa's concerns about the IEC's budget, but said the commission should be ready for early elections.