Villagers gathered at Wat Sao Thong over the weekend to discuss the plan to relocate the facility, along with a rubbish dump site, from tambon Baan Pom to tambon Mahaphram.
At the meeting, villagers were informed of the adverse effects of relocating the waste management facilities, such as health hazards and environmental degradation.
Mahaphram villager Anon Phokasit said residents will petition the NCPO to review its plan.
The move followed NCPO chief Prayuth Chan-Ocha's comments last Friday in his weekly programme Returning Happiness to the People, which focused on waste management.
In the progamme, Gen Prayuth announced he had approved a waste-management pilot scheme to be implemented in Ayutthaya province.
He said the people of Ayutthaya produce an average of 1,200 tonnes of waste per day, but only 700 tonnes are processed daily. This unmanaged waste has added up to 300,000 tonnes waiting in landfills.
Gen Prayuth said technology can turn the waste into electricity. Waste heat from an incinerator could be exploited to make clean energy for households.
He stressed that a waste-to-energy plant must be environmentally friendly and pleasing to eye, while helping generate job opportunities for locals.
He urged locals in the area where the new dump will be located to understand the need for construction work there, and to be positive about waste.
"We can turn rubbish into treasure. A lot of people make a decent living from trash," Gen Prayuth said.
Mr Anon said inspectors assigned by the NCPO had examined the area for the plant in tambon Mahaphram and found it suitable.
Mr Anon said technology to turn waste into clean fuel alone is not enough. A fully-integrated management system is needed to tackle the problem, he said.