Comparing the situation to that of former Rep. Anthony Weiner (D-N.Y.), Gingrich said voters would not forgive a lawmaker twice.
Last month, Radel pleaded guilty to cocaine possession and was sentenced to one year of probation. He recently entered a rehab facility in Florida. He has blamed his possession charges on an addiction to alcohol.
Weiner resigned from Congress in 2011 after lewd photos he sent to women through Twitter surfaced on the Internet. Revelations that his behavior continued long after he resigned helped tank his mayoral bid earlier this year.
Gingrich, who has survived his own controversies regarding his marriages, said there is a tendency during the holiday season for people to have Radel’s “family in their prayers.”
Speaker John Boehner (R-Ohio) and Republicans in Congress have not weighed in on whether Radel should resign. Boehner has said it is an issue between Radel, his family and his constituents.
However, Republican state officials — including the Florida GOP chairman and Gov. Rick Scott — have called on the freshman lawmaker to step aside.
Radel represents a solidly Republican district, but a number of former GOP opponents have expressed an interest in a primary fight against him if he decides to run in 2014.