Their comments came as Pretoria condemned Israel's ground offensive into the Gaza strip and several prominent South Africans of Jewish descent called for the country to cut ties with Israel.
"It is not a Muslim or Jewish crisis. It is a human rights crisis with roots to what amounts to an apartheid system of land ownership and control," Tutu said at a news conference on this year's annual summit of peace prize winners to be held in Cape Town in October.
Fellow Nobel prize winner and former president FW de Klerk said Israel and the Palestinians needed to work for peace.
"For the Israelis and Palestinians, the lesson to be learnt from South Africa is that there is no dispute which cannot be resolved by meaningful negotiation if there is the will on both sides to negotiate," said De Klerk, the last white president of South Africa, who will co-host the Nobel summit with Tutu.
"Yes, we condemn those who fan the flames, who launch the missiles against Israel, but missiles do not justify Israel's excessive response," he said.
"As an old man, my appeal to my fellow laureates and peacemakers is to step into the leadership void, to make your voices heard from all corners of the globe, to advocate or pressure your government and institutions to cajole, to persuade," Tutu said.
Mandela died on December 5 last year but his birthday today is commemorated internationally as Mandela Day.