The Democratic Alliance (DA) says Social Development Minister Bathabile Dlamini can't pick and choose which judge leads the probe into whether she should pay for the legal costs of the South African Social Security Agency (Sassa) debacle.

Dlamini filed papers to the court this week "conditionally agreeing" to a public inquiry into whether she is personally liable for the "fiasco", which eventually saw the contract with Cash Paymaster Services being extended by a year, eNCA reported.

DA MP Bridget Masango on Tuesday said her condition that former Deputy Chief Justice Dikgang Moseneke not lead the probe was not up to her to decide.

"In fact, she has no authority to place any conditions before the Constitutional Court and must accept [Moseneke] heading this inquiry if this is who the Constitutional Court decides to appoint."

Masango said the party welcomed the decision to hold a public inquiry, made by the court on June 15, as it will be the first of its kind in providing the public with an opportunity to hold Dlamini to account.

"The DA is hopeful that this will be a speedy and effective inquiry and will await the outcomes of this probe – it is high time that Dlamini was made to pay for her actions," Masango finished.

Dlamini filed papers to the court recommending her preferred three possible judges to act as referee in the inquiry, eNCA reported on Monday.

NGO Black Sash, the applicant in the case against Dlamini and the department also filed three.

They only agreed on two possible names to lead the probe, with Moseneke's name left off Dlamini's list.

Freedom Under Law (FUL), Sassa and National Treasury all supported the appointment of Moseneke as referee as friends of the court.

The Constitutional Court will have the final say.

In March, Dlamini told News24 that she was shocked that the court had ordered that one individual "could be singled out" for the situation at Sassa.

"This is the work of a collective, but if a court says at the end of the day: 'Take responsibility', we are going to ask: 'How should we take responsibility for the whole thing that has happened?'

"I personally think this time is not a time to say: 'No, I would not have agreed to this, I would have agreed to this [instead].'"

She however expressed that it was correct for her to be apologetic and follow the instructions of the court.

Dlamini, as minister, is the shareholder representative of Sassa as an entity, with its chief executive officer serving as its accounting officer.