Platoon member Ahmed Raza Khan reportedly told Harry to “forget about it” when the Prince phoned to apologise.
Harry was caught on film three years ago referring to Khan as “our little Paki friend”.
But Khan told The Sun the Prince was his friend and that he had no hard feelings towards him in the wake of the incident.
He said: “The Prince called me by a nickname which is usually very insulting but I know he didn’t mean it that way,” the newspaper reported. “We were close friends when we were training and I know he is not a racist.”
The two soldiers were said to have exchanged stories with each other about fighting the Taliban when Harry rang Khan to apologise.
The Ministry of Defence said the Chief of the General Staff had directed the Royal Military Police to investigate how the material entered the public domain.