The move came as the National Council for Peace and Order continues its ban on political gatherings of more than five people, despite calls from politicians to allow them to meet to discuss issues such as the draft constitution.
Prayut’s offer, on Thursday, includes the condition that military officers can attend the meetings.
Anusorn said the offer was tempting and party members were deciding whether to accept it.
And if they did, they would have to decide whether to invite all party members or just representatives from each region.
He said Pheu Thai would not abandon its responsibility to the people and the country, particularly now there were discussions about the draft charter.
The party had received a letter from the Constitution Drafting Committee asking it to urgently
forward its views and suggestions
on the charter draft.
Anusorn said if you viewed the constitution drafting process as being akin to constructing a house, then the builder must listen to the views of the homeowner, which in this case was the people.
The only structure where the occupants had no say in its construction was a prison.
He said the party had cooperated with the NCPO but some members wondered if the ban of political gatherings should continue to cover politicians or attending merit-making ceremonies where there were no speeches.