Edwards was paid £200,000 after being arrested in November, and he was suspended by the broadcaster until April, when he quit on medical advice.
On Wednesday, the 62-year-old veteran pleaded guilty to three counts of creating obscene photographs of children.
Culture Secretary Lisa Nandy told News at the Paris Olympics on Friday: “I believe he should repay his money.
“I believe that after being arrested on such serious charges in November, continuing to receive that salary until he resigned is wrong and not a good use of taxpayer money.”
The director general, Tim Davie, stated on Thursday that the company was aware of Edwards’ arrest for the most serious category of indecent photos of minors at the time.
He faced concerns about why Edwards was not fired at the time and why he was still paid the highest salary at News.
Mr. Davie had an urgent meeting with Ms. Nandy on Thursday to discuss his handling of the issue.
