Politicians said such an arrangement would severely erode the legitimacy of the election, which is expected to be held late next year and is supposed to return democracy to the country.
They also warned that the image of Prime Minister Prayut Chan-o-cha and the National Council for Peace and Order (NCPO) would be badly damaged.
Deputy Prime Minister Wissanu Krea-ngam agreed with politicians, saying the proposal for the NCPO to oversee the election could lead to credibility problems.
"The NCPO may have the power to do so but they must also consider whether it is appropriate. If the NCPO deals with the election directly through its military, police and civilian personnel, there may be criticism. There are risks involving legal and credibility issues," Wissanu said.
The NRSA's political reform committee proposed that the NCPO and Interior Ministry help the EC to ensure a free and fair election when voters go to the polls next year.