The petition was submitted at the end of a two-day session in which MPs listened to a report from a parliamentary commission on the security chaos pervading large parts of the territories, parliamentary sources said on Thursday.
The report accused the government of failing to contain the situation adequately or support initiatives from interior minister Nasr Yussef.
Parliamentary speaker Rawhi Fattuh said that parliament would fix a date to debate the motion "in less than three days".
Parliamentary sources said the meeting should take place next Thursday.
Fattuh said the motion was motivated largely by the
7 September assassination of Mussa Arafat, Palestinian leader Mahmud Abbas's military adviser and a former head of national security.
To pass, it must be approved by at least 43 of the 83 deputies sitting in the Palestinian Legislative Council, which seems unlikely.
Since the Palestinian uprising broke out in September 2000, large parts of the West Bank and Gaza Strip have slipped ever further into anarchy.
Abbas promised on Tuesday to end the internal chaos.