The president also said that a new law preventing foreign ownership of land in South Africa applied only to agricultural properties and not to private residences.
Zuma was reacting to concerns by some white South Africans after he told a rally of his ruling African National Congress that all South Africa's troubles began when the first whites landed more than 300 years ago.
"South Africa belongs to all who live in it, black and white," he told parliament on Thursday, quoting the ANC's Freedom Charter, which was adopted during the fight to end the white racist system of apartheid.
Breaking away from his written speech in response to debate on his State of the Nation Address last week, he said: "We are a rainbow nation. Nobody will chase you away.
But, he said, he would never stop talking about history because South Africa's children should know the country's past to ensure that mistakes were not repeated.
Zuma's off the cuff remarks won enthusiastic applause from the audience.
It was a redemption of sorts for the president, who has been under fire over the past week since security forces were called into parliament to evict lawmakers who disrupted his annual address by accusing him of corruption.
Addressing the uproar in parliament for the first time, he called for all parties to preserve the dignity of the national assembly.
Radical lawmakers of the Economic Freedom Fighters, who led the disruption last Thursday, remained silent and seated throughout his speech.
