Soon after The Idaho Statesman in Boise published an article in which the men made the allegations Sunday, Craig's office issued a statement criticizing the newspaper, CNN reported.
"Like its previous coverage, these latest allegations are completely false and have no basis in reality," the statement said. "In fact, the paper itself states that these baseless accusations contain no definitive evidence, yet they still decided to print them anyway."
The 62-year-old was arrested in June in a sex sting at a men's washroom at the Minneapolis-St. Paul International Airport, and two months later pleaded guilty to a misdemeanor disorderly conduct charge.
He has a petition before Minnesota courts to let him withdraw his plea, which he later called a mistake as he hadn't consulted an attorney.
On Aug. 28, he called a news conference to speak out against the allegations.
"I am not gay. I have never been gay," he said.