"Given the timeframe that we have till the end of the month, I am confident that the court is going to pull out all stops to deal with this matter," Ramaphosa told the National Assembly in response to a question from Democratic Alliance leader Mmusi Maimane.
"Let us allow the court to deal with the matter, let us allow the department to deal with this matter. I am absolutely certain a solution is going to be found."
He stressed that the Constitutional Court had "well-endowed minds" that would do their best to ensure that some 17 million welfare grants reach beneficiaries every month once the contract with the current service provider, Cash Paymaster Services, expires on March 31.
Maimane had asked whether Ramaphosa would back calls for Social Development Minister Bathabile Dlamini to be fired over her handling of the situation.
He did however say that he regretted what transpired this week when Dlamini appeared before Parliament's watchdog public accounts committee (Scopa).
The minister outraged MPs when she read out a statement and then sought to evade questions, telling committee chairman Themba Godi that she needed to attend a special Cabinet meeting on the issue.
Godi detained her for some two hours to answer questions, but Dlamini declined to give details of her recent negotiations with CPS for a new contract, and blithely blamed officials for not acting sooner to avert a crisis.
She claimed that the South African Social Security Agency (Sassa) left her in the dark until late last year as to the fact that it would not be ready to take over grant disbursement from April. Dlamini will now have to provide more detail to the Constitutional Court than she did to the committee. Chief Justice Mogoeng Mogoeng on Wednesday gave the department and Sassa five days to tell the court who decided that Sassa would not be ready and when it had become apparent to them that this was the case.
Ramaphosa told MPs that Dlamini had approached the Constitutional Court with "with a particular prayer". In fact, Dlamini has decided not to seek the court's permission to extend Cash Paymaster Services' contract to distribute grants, relying on the technical distinction that she was not seeking an extension but a new contract with the company.
Sassa had planned to approach the court, in line with its oversight function on the issue, but was ordered by the minister to withdraw its application. Instead, a declaration of intent to enter a new contract with CPS was filed with the court.
The minister is adamant that only the company would be able to pay out grants in the near future, and expects National Treasury to approve a deviation from normal procurement rules because no other bids have been entertained.
Her critics say the crisis she is seeking to avert by signing an eleventh hour deal with CPS was self-made. In 2013, the Constitutional Court invalidated the contract with CPS because it resulted from a flawed procurement process.
However it suspended the ruling for the full duration of the deal, so as not to disrupt grant payment.
The Black Sash lodged an application for the court's oversight over the process to be reinstated. Dlamini on Thursday indicated that she would not oppose it and undertook to comply with Mogoeng's order.