Land Reform and Rural Development Minister Gugile Nkwinti is considering asking Cabinet to consider exceptions to the 1913 land claim cut-off date.
Land belonging to the descendants of Khoi and San in the Eastern and Western Cape was forcibly taken from them long before then, he said.
Nkwinti said in his department's budget speech in Parliament that the call by the descendants of the San and Khoi to beyond the date of the 1913 Land Act was "fair and just".
"Their land in what is now the Western and Eastern Cape was forcefully taken from them way before the 1913 act. And, whatever land that is returned to them is non-productive, urban, land.
"We are persuaded to consider asking Cabinet to, while retaining the current cut-off date, consider exceptions to the law."
The department had interacted with more than 3000 people between August, 2010, and March, 2011, after the Cabinet established an inter-ministerial committee to study a proposal on whether to make exceptions to the cut off date.
A preliminary report had already been submitted to Cabinet.
"Our people complain that the period for the lodgement of land claims was too short, with the result that research and verification were very poor; and, that the 1913 cut-off date is too close," he said.
"They call on the government to consider re-opening the lodgement date and extending the cut-off date.
"This call may appear to be radical, but if one considers the social consequences... it is a fair and just call."
Descendants of the Khoi and San have asked: "What is in this for us, the original people of this land?" Nkwinti said.
He said the ANC had been "magnanimous" and generous in victory, almost to a fault" on its land redistribution policy.
He said it was committed to redistributing 30 percent, or 24.5 million hectares, of South Africa's agricultural land by 2014.
In 1994, South Africa had approximately 82 million hectares of white-owned agricultural land.