A South African dentist and his cousin, a Muslim cleric, have denied having any links to al-Qaeda or the Taleban.
They were put on a UN Security Council terror list after US accusations they were al-Qaeda "facilitators and terrorist financiers".
Dentist Junaid Ismail Dockrat and cleric Moulana Farhad Ahmed Dockrat have threatened legal action to clear their names.
They face a travel ban and having their assets frozen.
The South African government has been in contact with the US over the allegations, the South African Sunday Times reported.
The US document claimed that the pair raised money for an al-Qaeda associated group in Pakistan and that Junaid Dockrat recruited for al-Qaeda in 2004.
Junaid Dockrat dismissed the allegations as being "patently false and devoid of any merit".
"I am a law-abiding citizen and am prepared to contest these allegations in a court of law," he said.
"I have full confidence that our government will not yield to pressure to act in a manner that will deprive me of my constitutional rights and my right to be presumed innocent."
Moulana Dockrat, who was detained with his son while on a trip to Gambia last year, also denied the allegations.
"If one is a Muslim and has Muslim interests at heart, one is considered a terrorist by the United States," he said.