Mr Trumptweeted that Griffin should be "ashamed of herself" and that his 11-year-old son, Barron, was "having a hard time with this".
Griffin also called the president a "fool" and said that she believes attention on her photo is a distraction from more important government issues.
Griffin stood by her apology and said she never intended the image to come across as a threat to the president, or suggest that she advocated violence against anyone.
Griffin reiterated on Friday that she had made "a terrible mistake", saying the bloodied head image was meant as a retort to comments aimed by Mr Trump at U.S. journalist Megyn Kelly during the election campaign. "I went too far", she said in a video posted to Instagram late Tuesday.
In addition to her canceled tour dates, Griffin has also been fired from her gig co-hosting CNN's New Year's Eve special with Anderson Cooper.
A reporter asked the 56-year-old comedian if she feared for her career now.
Griffin used the press conference - itself riddled with jokes and less-gory jabs at Trump - to lash out at what she said was an unprecedented campaign to ruin her that started in the Oval Office. "I feel disgusting. I did not think people would try to murder me or mobilize other people to murder me".
Griffin, who asserted that she has been contacted by the Secret Service, said the Trumps are "trying to ruin my rights forever".
She said: "I'm not laying down for this guy". "When you consider some of the atrocities happening in the world today, a photo opportunity like this is simply wrong and makes you wonder about the mental health of the person who did it". "Forever. You guys know him - he's never gonna stop".
"If you don't stand up, you get run over", she said at the press conference in Woodland Hills, Calif.
Gorin then addressed the apparent secret service investigation into the photoshoot, saying he expects it to be closed shortly and for Griffin to be cleared.
Griffin's attorney Bloom explained the motivation behind the controversial image, which was motivated by the President's comments about Megyn Kelly.