Chartthaipattana and Pheu Thai voiced support Tuesday for the Future Forward Party's initiative to amend or even scrap the 2017 constitution.
Varawut Silpa-archa, a core member of the Chartthaipattana Party, said there were certain elements in the charter that could be amended to make them better and more practical.
According to Mr Varawut, there are certain limitations to the election system, the political party system and even mechanisms in the national administration that should be addressed.
He stressed that it was not unlawful for political parties to include charter amendments as part of their policy platforms.
Speaking after the Future Forward Party's general assembly on Sunday, Piyabutr Saengkanokkul, the party secretary-general, said the party would seek to amend Section 279 of the charter during its first day in parliament.
This section legalises all of the orders, announcements and actions of the NCPO.
Meanwhile, party founder Thanathorn Juangroongruangkit said he would pardon all political prisoners if the party gains power next February when the election is due to take place.
Mr Varawut suggested that a constitutional drafting assembly be established to proceed with charter amendments.
He cited the drafting process of the 1997 charter which was made possible by amending Section 211 of the 1991 constitution to allow the establishment of a charter-writing panel.
"There was strong opposition at that time but political parties made it through. We've demonstrated we can do it together. So I believe we can do it again, together," he said.
On Monday, Pheu Thai key member Watana Muangsook voiced support for the Future Forward Party's initiative to scrap the 2017 constitution.
The regime critic said he agreed with the policy of creating a new charter because the current one was undemocratic and passed by a referendum that lacked transparency.
According to Mr Watana, the regime used every trick in the book to get the charter passed, including pressing charges against critics and dispatching military officers to highlight "good points" to the public, he said.
The Pheu Thai member also pledged himself as an ally of the new party to fight against dictatorship and for the return of power to the people.
