Should the editor refuse, the popular Chinese daily will face three to six months' suspension.
The DAP supremo said this at a conference in Parliament lobby this morning after leading a walkout from Dewan Rakyat by Pakatan Rakyat members of parliament.
This was in protest of deputy speaker Ronald Kiandee's decision against allowing a debate on a motion by the Home Ministry.
Hishammuddin denies claim
In an immediate response to Lim's allegation, Home Minister Hishammuddin Hussein denied that the China Press editor has been told to resign.
He told a press conference in the Parliament lobby that the ministry has only issued a show-cause letter, and that the newspaper has submitted a repy.
""As far as I know the editor has not been asked to resign. They (Pakatan MPs) will sensationalise and politicise any issue... It's not at all related to the motion that was brought today," he said.
"I took notice that not all the PR (Pakatan) MPs joined in the walkout. Even they (sic) don't agree with it."
In 2006, China Press was faced with possible suspension following its report over the nude-squat scandal, in which it mistakenly claimed that the individual concerned was a Chinese national.
The scandal, sometimes referred to as Squatgate, triggered a diplomatic tiff between Malaysia and China.
The powerful Internal Security Ministry was reportedly appeased only after two of China Press' top editors were axed over the matter.