The Hawks are probing four cases of treason linked to disinformation about the Land Expropriation Act.
The cases were opened by political parties.
While Hawks head Gen Godfrey Lebeya, did not want to say who the cases were opened against, he said the cases concern "some individual that may have crossed the border to go and communicate some of the things that are perceived to be in the direction of high treason. I don't want to mention names of [the] organisation".
Lebeya said their investigation was at the initial stage.
There have been growing calls for Afrikaner lobby group AfriForum to be charged with treason.
Last month, the MK Party filed a treason complaint against AfriForum, after an executive order signed by US President Donald Trump, citing disapproval of SA's land expropriation policy and its genocide case at the International Court of Justice against Washington's ally Israel.
The US then said there were plans to develop a strategy to offer Afrikaners refugee status.
We don't discriminate, anyone who commits a crime must know we will be doing that without fear or favour or prejudice.
— Hawks head Gen Godfrey Lebeya
AfriForum is in Washington to meet Trump's representatives amid tensions between US and SA.
This resulted in President Cyril Ramaphosa saying AfriForum and Solidarity should focus on solving SAs problems internally rather than taking their grievances abroad.
On Monday, Lebeya said the Hawks were working with the National Prosecuting Authority (NPA), which will determine if there is a case.
"Those type of crimes, you have to be careful in the way that you collect the evidence. When the time comes, at the conclusion of the investigation, the National Prosecuting Authority will determine whether what we have collected is sufficient for anyone to be secured before court.
"On our own we just don't go and arrest. We are working closely with the NPA to check whether the content of the affidavits that we shall have put together as well as other material evidence is sufficient for the NPA to make a decision to proceed with the prosecution," he said.
Lebeya said if there is enough evidence then the NPA will direct them to secure the individuals' attendance before court.
"We don't discriminate, anyone who commits a crime must know we will be doing that without fear or favour or prejudice," Lebeya said.
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