Since Edwards, the former Democratic senator and presidential candidate, was indicted on federal campaign finance charges last week, he now says giving a deposition in a related civil case would risk self-incrimination.
Edwards denies illegally using campaign funds to cover up his affair with mistress Rielle Hunter and their child.
In the civil case, Hunter is suing former campaign aide Andrew Young, who wrote a book about the affair. She says the tape is hers.
Judge Carl Fox in Hillsborough N.C., ordered Edwards in April to give Young's lawyers a private deposition under oath.
In a document filed Thursday, Edwards' attorneys say Young is cooperating with the prosecution and may testify against him, The Charlotte Observer reports.
Edwards had Young claim he fathered Hunter's daughter but later acknowledged the girl was his.