The couple is demanding Mamabolo issue a public apology for claiming that Malema abused his wife and admit that he lied.
Mantwa described the abuse claims as vexatious, misplaced, spurious and untrue.
She says the statements amount to emotional abuse of herself and her children, who she says are being mocked at school.
The couple has threatened to sue the ANC MP for R1 million if he fails to make the apology.
But Mamabolo, who made the claims during the Sona debate on Tuesday, said he would not apologise, instead daring the Malema family to meet him in court.
He said he never made the claims outside of Parliament.
“I never spoke to anyone outside. I am going to prove my facts in court,” he said.
The ANC has called on its caucus in Parliament to investigate the use of gender-based violence to score political points.
Meanwhile, as the debate continued on Wednesday, the DA said it wants Energy and Mineral Resources Minister Gwede Mantashe fired if he does not fix Eskom soon.
DA MP Kevin Mileham said President Cyril Ramaphosa was not bold enough to take action.
“SONA was the last chance for the ANC to do the right thing and announce the immediate splitting and privatising of Eskom,” he said.
“What we got instead were small changes, small concessions, small retreats - too little, too late - if they come to be at all.”
Mileham said the DA-led City of Cape Town was going ahead with a court action to force the issue of independent energy providers because “whenever anyone speaks about renewable energy, in any context, Minister Mantashe accuses them of being a lobbyist.”
He called on Ramaphosa to open up the electricity market, saying the private sector could deliver better, cheaper and more efficiently than Eskom.