They have urged People's Democratic Reform Committee secretary-general Suthep Thaugsuban to clearly explain how the council would operate.
A 50-year-old military officer taking part in the anti-government protest at the government complex yesterday, said Mr Suthep's people's council proposal and the interim government still posed "many questions".
The officer, who identified himself only as Anucha, said the council still lacks legitimacy since there is no law supporting its establishment. "Mr Suthep must come up with a clear answer to the public [on how the council will be formed], while the Democrat Party has to ensure they will not get involved with the selection of council members," he said. "All political parties also should be reformed, to avoid further conflict."
On Tuesday, Mr Suthep for the first time spelled out what he meant by a "people's council".
He said he wants to invoke Section 7 of the constitution, which would lead to the installation of a royally appointed prime minister and cabinet.
Mr Suthep said people from all walks of life will then choose representatives from various professions to form the council. The council would work out policies and draw up legislation, including charter amendments. His idea has been criticised by academics and the Pheu Thai Party, who say the move would be an affront to democracy.
Mr Anucha, however, believes confusion over Mr Suthep's proposal will not shrink the number of protesters because they share the same goal of toppling the Yingluck Shinawatra government.
Worakit Pirookunakarn, 55, a businessman from Chon Buri province, who also rallied at the government complex yesterday, echoed Mr Anucha's concerns. He said details about the selection process of the council were unclear, adding these shortcomings would weaken the council once it is formed.
However, Mr Worakit said if the selection process is transparent and accepted by all sides, the council will be able to solve the country's political problems.
Saifon Sukhonthapan, 50, from Pathum Thani province, said she supported Mr Suthep's people's council plan, since the House could not function properly. She said it doesn't matter if there is no law to support the council.