Zuma was speaking to journalists at Tuynhuys after talks with his Nigerian counterpart Goodluck Jonathan.
The president said he shared with Jonathan "the same vision" of a conflict resolution mechanism led by Africans.
"The need for an intervention brigade has become more crucial in light of the situations of instability in the Central African Republic [CAR], eastern DRC [Democratic Republic of Congo], and Mali, where decisive intervention is needed," he said.
The issue deserved attention as the continent prepared to celebrate half a century of formal pan-African integration, Zuma said. He was referring to the birth of the Organisation of African Unity in May 1963.
"As we mark the golden jubilee, on May 25, it is crucial to build a stronger and well-resourced AU to take forward the promotion of peace, security and the safe economic advancement of our continent.
"Part of the capacity by the AU is the establishment of the African standby force, for rapid deployment in crisis areas without delay."
Nigeria unhappy about SA's decision
Zuma's remarks followed suggestions in diplomatic circles that Nigeria has demanded greater co-operation from Pretoria on regional security and military operations.
The Nigerian government was reportedly unhappy about South Africa's unilateral decision to deploy troops in the CAR, where 13 South African soldiers died in clashes with rebels in March.
Speaking alongside Zuma, Jonathan said it was imperative that Africa's two biggest economies work together for the good of the continent.
"Nigeria and South Africa must come together, must work together to help the continent of Africa. If we refuse to move the continent, to give direction, we will be considered failures and we do not want to be entered into the Guinness Book of Records of failures."
Jonathan is paying his first state visit to South Africa and will attend the 23rd World Economic Forum on Africa in Cape Town this week.
The governments of South Africa and Nigeria signed nine agreements and memoranda of understanding on Tuesday, pledging co-operation in, among others, defence, gas exploration and power sector development.
Nigeria and South Africa also signed an agreement waiving visa requirements for holders of diplomatic passports. The move comes amid unhappiness in Abuja over strict travel regulations for Nigerians who want to visit South Africa. – Sapa