The welfare system - which includes more than 11m child support grants - is a lifeline for the country's poor.
Mr Zuma told parliament his government was "doing everything possible" to ensure welfare payments are distributed.
He also defended Social Development Minister Bathabile Dlamini, who has criticised by South Africa's Constitutional Court over the crisis, amid calls for her to be sacked.
It comes after a 2014 decision that the contract between the government and service provider Cash Paymaster Services (CPS) was unlawful.
The government had until the beginning of April this year to take over responsibility for social service payments or find a new provider - but it has done neither.
CPS has said the issue must be resolved by the end of today or April's welfare payments may not be made on time.
source: bbc