While Craig has apologized for keeping the June arrest at the Minneapolis-St. Paul International Airport a secret, many Idaho conservatives have begun calling for the senator's resignation, CNN reported Wednesday.

"I believe he should resign because I believe character is an extremely important qualification for public service," Idaho Values Alliance member Bryan Fischer said. "And I believe the senator, by his own admission, has acknowledged that he has fallen short of the standard that we should expect from public servants."

Craig was arrested on June 11 at the Minneapolis airport for allegedly attempting to engage in "lewd conduct" with an undercover male police officer.

After news of the arrest broke earlier this month, top Republicans in the U.S. Senate called for an Ethics Committee investigation into the incident.

CNN said Craig has attempted to downplay the incident, alleging he is not gay and is the target of a political "witch hunt."