Speaking at the opening of the National House of Traditional Leaders in Cape Town, he called on members to put together a team of "good lawyers" to take advantage of the recently-passed Restitution of Land Rights Amendment Bill.
The measure, approved earlier this week by the National Assembly, seeks to re-open the land restitution process with a new December 31, 2018, deadline for land claims.
Deviating from his set speech, Zuma said "history was made" with the passing of this legislation. Many who were excluded by the previous cut-off date -- December 31, 1998 -- now stood a chance of regaining their land.
A "critical problem" was that while the process of taking land from South Africa's inhabitants had taken centuries, "when we are supposed to address this matter, we are only given a few years to deal with it".
The previous process had "excluded many people", particularly those in rural areas who did not receive Government Gazettes, had not been aware of the deadline, and were therefore "automatically" excluded.
"We must re-open [this matter]. This law will do so. I'm hoping that during this period, we will also do one thing -- look at the act.
"Because the quicker reading of the act, being not a lawyer, is very biased. Those who are claiming land, they have got to go into minute detail to prove this was their land. Those who are owning the land have to do very little to stop the claim."
The matter needed to be looked at by lawyers.
"I think those who are claiming should find good lawyers to help address this matter."
He called on traditional leaders to pool their resources to help claimants.
"It is a matter that, in my view, you could put together your resources to look at this law, to look at the claims on behalf of your people, so that no-one is left outside," Zuma said to applause.
In 1913, the day after the notorious Land Act became law, black South Africans had woken up to discover they had no land.
They were plunged into poverty, he said.
"Therefore the land is something we must take seriously as the opportunity presents.
"Therefore I say we must look at the law. It must not be very difficult for us to prove that this is our land, and be easy for those who say I bought this land."
He repeated his call on traditional leaders to put together a team of good lawyers to go into this process once again with a fine toothcomb so nothing was left unattended.
Earlier, Zuma said government had spent about R20 billion, since May 2009, in acquiring about 1.8 million hectares of land for restitution and redistribution purposes.
"Work continues to acquire more land, and to improve the ownership patterns of land in our country, to correct the historical injustice of 1913."
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