In the letter, Tiegs claims her statement thought to be about Graham was more general, saying she was asked "a generic question, and I said that I did not love it."
"My answer was based on health concerns because of our nation's increasing problems with weight linked to diabetes, heart issues and cancer. At no time was I thinking of a specific person," she said.
"What has ensued is yet another 'manufactured media feud' that is needed to feed websites and empty air time," she added.
Tiegs claimed she was not connecting beauty with weight or size, revealing she herself had a "37-inch waist."
"Please accept my deepest apology if you were offended or in any way think I was referring to you. I commend you on the positive influence you have on helping women to love themselves," the former model wrote.
The letter comes shortly after Graham reportedly shrugged off Tiegs' initial comments. "Oh, whatever, another one of these ladies," she said earlier this week at Paris Fashion Week.
"What's great is that -- the fact that she said it -- it means that other women think like her," she added. "And what that means is that we really need to change the industry," she added.