Hor Namhong said Monday he had briefed diplomats on the request and would travel to New York to report to the Security Council.
Association of Southeast Asian Nations is trying to negotiate end to clash between two countries' forces.
The Cambodian government says part of an 11th-century Hindu temple has been damaged by cross-border artillery fire from the Thai army.
Government spokesman Phay Siphan said Thai political strategists have used the border situation to unseat two prime ministers.
Friday's fighting included the firing of multiple rockets from vehicle platforms and from tanks.
The Sam Rainsy Party holds 26 of 123 National Assembly seats; the Human Rights Party holds three.
According to reports, Thai Foreign Minister will bring a message to Cambodia Friday saying Thailand has no intention of war.
Cambodia is facing an overcrowding of its jails, with an estimated 14,000 prisoners across the system in 2010.
Mu Sochua had her immunity stripped by the Assembly in 2009, after she was sued by Prime Minister Hun Sen for defamation.
Wednesday’s statement was made to clarify misunderstandings in the media regards to cases 003 and 004.