"It's his burden to make that case going forward," said Mr. Davis.
The Republican senator inadvertently became a character in the scandal after Mr. Sanford repeatedly apologized to him and to "the Tom Davises of the world."
Mr. Davis, who attended the Capitol rotunda news conference, has subsequently been interviewed on ABC News.
"Tom Davis came over to the house. He drove up from Beaufort," said Mr. Sanford, frequently struggling to keep his composure. "And he has been an incredibly dear friend for a very long time."
Mr. Sanford and Mr. Davis have been friends for about 30 years, starting in college. Their families have vacationed together and their children are friends.
"I very much believe in the man, and I very much believe in the ideas he espouses," Mr. Davis said Thursday.
"There is a profound sense of disappointment at the pain I know he's caused Jenny and their four children. My prayers are with them. Hopefully they can put things back together."