The Indian-born Gupta brothers Ajay, Atul and Rajesh are known to be close to former South African President Jacob Zuma. His son, daughter and one of the former President's wives worked for the family's firms, according to media reports.
The Gupta brothers have been accused of wielding enormous political influence in South Africa, with critics saying that they tried to "capture the state" to further their own business interests.
The family allegedly used its relationship with Zuma to influence state contracts, Cabinet appointments and secure several lucrative deals in the country. The former President, however, claimed that he never broke the law in his dealings with the Guptas.
In the affidavit submitted to the commission, headed by Deputy Chief Justice Raymond Zondo, Ramaphosa on Friday said that his meetings with the Gupta brothers had been "inconsequential", South Africa's Times Live reported.
Ramaphosa said he had met with two of the Gupta brothers on "three or four occasions".
"My interactions with the Gupta brothers were at events where nothing of any consequence was discussed. I never engaged with them beyond the basic greetings, pleasantries and common courtesies."
The President said that the "only occasion where matters of substance were discussed was when the Guptas met the African National Congress (ANC) officials to discuss their situation in relation to closure of their bank accounts and at which was also raised the controversy around them and their relationship with Zuma", IOL News reported.
Ramaphosa also detailed another instance in April 2016 when Rajesh Gupta had met him and made a presentation on the Gupta family's business model.
The President said that he had also voiced concern over landing the family's private jet full of wedding guests at South Africa's National Defence Force Waterkloof Airforce Base in 2013, Business Day newspaper reported.
"I stated that they had, through their actions, placed the former president in an invidious position," the affidavit read. "Tony (Rajesh) Gupta's reaction was that permission for the plane to land was obtained and given by the Indian High Commissioner."
Ramaphosa's affidavit came after the commission wrote to him and all members of the Cabinet to state whether they had any meetings, or interactions or dealings with any of the Gupta brothers and if that had happened, to detail the nature of the interactions.
( With inputs from IANS )