Most Revd Justin Welby delivered a sermon on walking in the Spirit during Evensong at St George's Cathedral in Cape Town when he warned against both abandoning the law and becoming legalistic.
He also warned of division, saying: "When we do not walk by the Spirit the church is divided; for the Spirit brings us as one to Jesus, to love inexhaustible and hope that never fades."
Recognising the contribution the Church in South Africa made towards ending apartheid and supporting the post-apartheid Truth and Reconciliation Commission, he said religious leaders are to be political but should avoid party politics.
On the New Year's visit, the Archbishop was accompanied by his wife Caroline Welby and Southern African Archbishop Most Rev Dr Thabo Makgoba.
On Twitter Dr Makgoba posted a picture of Archbishop Justin accompanied by a group of children and wrote: "Archbishop Justin on his knees with kids, before visiting two townships to feel and see the two faces of Cape Town."
Earlier, he wrote the two leader's families were "enjoying the sun and water together in Cape Town. New Year's Day 'Sabbath' rest".
Taking to Twitter himself, Archbishop Justin spoke of the "privilege to meet Archbishop Emeritus @TheDesmondTutu and family - inspired by his challenge to serve Christ above all personal interest."