"I think she did the right thing asking for forgiveness and acknowledging that this was a horrible mistake, so I think she can," the Minnesota Democrat and former "Saturday Night Live" writer told CNN's Alisyn Camerota on "New Day."
Griffin apologized on Instagram
on Tuesday for the photo that some say encouraged violence against the President.
"I'm a comic," said Griffin, a frequent Trump critic. "I cross the line. I move the line, then I cross it. I went way too far. The image is too disturbing. I understand how it offends people. It wasn't funny. I get it."
She said she'd ask celebrity photographer Tyler Shields to remove the photo and rejected the idea that she was encouraging violence against the President.
"I beg for your forgiveness. I went too far," she said in the post on Tuesday. "I made a mistake and I was wrong."
Trump weighed in
Wednesday, calling her actions "sick."
"My children, especially my 11 year old son, Barron, are having a hard time with this. Sick," he tweeted.
Franken said he still plans to appear with Griffin in July as part of a promotion tour for his new book. Minnesota GOP Chairman Jennifer Carnahan posted a statement Tuesday on her Facebook page calling on the senator to cancel the Beverly Hills event.
Franken cited Griffin's apology in explaining his decision.
"Kathy's a friend and she's a terrific comedian, but this had no business being in our public discourse," Franken said. "And I talked to her. She has apologized -- a real, fulsome apology. She's actually begged for forgiveness, and I believe in forgiveness."
Griffin, who had regularly participated in CNN's annual New Year's Eve coverage, was universally criticized for the grotesque image.
A network spokesperson called the image "disgusting and offensive" soon after it became public, and the network announced Wednesday it had terminated its agreement with Griffin to appear on CNN's New Year's Eve program.
CNN's Anderson Cooper, who had co-hosted the network's New Year's Eve coverage with Griffin, also condemned the photo.
"For the record, I am appalled by the photo shoot Kathy Griffin took part in. It is clearly disgusting and completely inappropriate," he tweeted.