In a court filing obtained by ABC11, Edwards says answering questions under oath would violate his Fifth Amendment right not to incriminate himself.
Hunter worked as a videographer in 2006 for Edwards' political action committee. Edwards initially denied an affair and later denied fathering a child with Hunter. He has since admitted to both.
Hunter sued former Edwards' aide Andrew Young and his wife for invasion of privacy in an effort to get the sex video. She has said she attempted to destroy the video tape by pulling it out of its cassette box before storing it in a box of private belongings.
Young, who has said he helped keep Hunter in hiding for Edwards during the 2008 presidential campaign - and later wrote a book about the experience - contends the tape was found amid trash that Hunter left behind in a home that he was renting.
Edwards testified in a February deposition, but refused to answer some questions.
Superior Court Judge Carl Fox ordered a new deposition for later this month. Edwards' filing asks the deposition to be delayed until the criminal case against him is resolved.
Edwards' criminal trial was originally set for July 11. A joint motion filed in federal court Friday delays that indefinitely.