The paper said it accepted the criticism and would review the service
The owners of a Taiwanese newspaper have been fined $15,500 (£9,300) for using lurid online animations to illustrate crime stories
Apple Daily's Motion News was deemed to have broken child protection laws by using the format to reconstruct stories of child abuse and violence.
Hau Lung-ping, mayor of the capital, Taipei, said he respected press freedom but the media had to show restraint.
The paper apologised and said it would tone down the animations in the future.
The Motion News service, published by Next Media, was launched last week online and on mobile phones.
Instead of using images or video on its stories, it posted computer animations which recreated robberies, rapes, violent attacks and child abuse in vivid detail.
The violence on display had attracted criticism. "By my definition, this cannot actually be called news," Bonnie Peng, chair of the National Communications Commission (NCC), was quoted by the China Post as saying.
Mayor Hau Lung-ping said he had been concerned by content of the site and warned that the media had to be aware of its social responsibilities.
"News media must not air improper content with no restraint on the pretext of news freedom," he told a news conference in Taipei.
He added that officials would continue to monitor the site and more fines would be imposed if it broke the law again.
Apple Daily published a six-point apology on its front page on Thursday, saying it welcomed the suggestions for how to improve.
Editor Ma Wei-min said Motion News would be reviewed but not discontinued.
"When it comes to controversial content, perhaps we would no longer reproduce the scenes in such actuality," he told reporters.