Speaking after allegations about his private life were published in newspapers, he accused political opponents of trying to smear him.
Mr Ramaphosa is planning to contest the leadership of the governing African National Congress (ANC).
President Jacob Zuma steps down from the post later this year.
Mr Ramaphosa's private emails were apparently hacked into to prove an affair between him and a medical doctor.
The emails reportedly suggest he also had a series of affairs with young women, and had unprotected sex.
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The Deputy President
admitted he had had an affair with a doctor eight years ago, but said the other women named in connection with him were students he and his wife supported to further their education.
Mr Ramaphosa had tried to block publication of the allegations in the courts, arguing that his private affairs were not in the public interest.
He also said he would ask the country's inspector general of intelligence to investigate the hacking of his emails.
I had a relationship with only one person and it ended. I dealt with it with my wife," Mr Ramaphosa told South Africa's Sunday Times.
I have to be prevented at all costs from ascending to the position of president of the ANC. Some have even said it will be over their dead bodies.
I have not committed any crimes, I have not stolen any money, I have not looted state resources. But I am being targeted and smeared."
The 64-year-old and Mr Zuma's ex-wife Nkosazana Dlamini-Zuma are the front runners to replace Mr Zuma when he steps down as ANC president in December.
The leader of the ANC automatically becomes the party's candidate for president of the country.