The decree imposing emergency law is due to expire on March 28.
The CMPO on Monday said protests by the People's Democratic Reform Committee (PDRC) and others, and related violence, have subsided.
A statement from the centre added that lifting the emergency decree would be good for the country's image, investment, tourism and other businesses.
The ISA will take effect immediately if the caretaker cabinet approves the CMPO's proposal at its meeting on Tuesday.
A new centre with a similar structure to the CMPO would be set up to oversee military, police and civilian operations under the ISA. Its command headquarters would still be at the Office of the Narcotics Suppression Bureau on Vibhavadi Rangsit Road.
Despite a scaling back of anti-government protests, the PDRC is training up to 2,500 guards to provide security for its demonstrators at Lumpini Park, according to the CMPO.
The CMPO statement said the forming of such a security force is illegal.
"The CMPO calls for all concerned, be they the PDRC, United Front for Democracy against Dictatorship (UDD) or other groups, to avoid organsing such training because doing so will only increase political tensions.
"Please take into consideration the issue of law and order for the common benefit of society," the statement said.