Edwards, who was the deputy chief of the National Security Section in Virginia’s Eastern District, said he was resigning to "uphold my oath to the Constitution and the country."
Special counsel David Weiss on Thursday indicted the younger Biden on tax charges.
"It was a senseless tragedy," Chad Wolf said on the "Just the News, No Noise" TV show. "It's also an indictment of the Biden administration."
Trump said last week that he expects to be indicted in Willis' probe.
The indictment dropped the allegations that Trump attempted to pressure the U.S. Justice Department to overturn the results of the 2020 election, but does include charges of conspiracy to defraud the U.S., conspiracy to obstruct an official proceeding, obstruction of an official proceeding and conspiracy against right.
Trump announced the indictment earlier this week on TRUTH Social, calling it a "dark day" in American history.
Indictment alleges politicians engaged in exchanges with a businessman seeking a tax abatement for a property.
In a prior interview with radio host Hugh Hewitt, Pence said he was "deeply troubled" by the indictment.
The presidential candidate's comments come shortly after special counsel Jack Smith announced a second indictment of Trump in relation to his efforts to challenge the 2020 presidential election results.
The former president's attorneys were reportedly told to expect him to be indicted.