The six opposition parties have refused to be part of the reconciliation process, saying the government lacks sincerity in fostering unity.
Speaking after a meeting between the opposition parties on Tuesday, Pheu Thai leader Sompong Amornvivat said they would not join the proposed reconciliation panel unless the protest movement also takes part.
The government must show sincerity in creating a climate of reconciliation by stop harassing or taking legal action against its opponents without good reason, Mr Sompong said.
Chaithawat Tulathon, secretary-general of the Move Forward Party, said the opposition parties agreed with efforts to bring about unity, but the process cannot proceed as long as those who hold different views continue to be persecuted.
Prachachart Party leader Wan Muhamad Nor Matha said the government must show it was serious about charter amendments, which would help ease the political conflict, particularly changes to curtail the power of the 250-member Senate appointed by the now-defunct National Council for Peace and Order.
He was referred to Section 272 of the charter, which allows senators to join MPs in voting for a premier.
Songkhram Kitlertpairote, leader of the Puea Chat Party, said the government lacked sincerity in the reconciliation process. It is clear that the government representatives to sit on the unity panel will only create more divisions, he said, adding that if the opposition parties join the panel, this would legitimise government actions.
Last Friday, Prime Minister Prayut Chan-o-cha insisted that national security should be part of the reconciliation process as he confirmed Deputy Defence Minister Chaichan Changmongkol would be one of two government representatives on the panel.
Gen Prayut said he nominated Gen Chaichan because he believed the views of security officials should be heard. He did not expect Gen Chaichan's participation would cause controversy.
It had previously been reported that the government had named Terdpong Chaiyanant, a Democrat Party MP, and Suporn Atthawong, vice minister to the Prime Minister's Office, as its representatives on the reconciliation panel.
However, concerns were then raised about Mr Suporn's participation. A former key figure in the red-shirt United Front for Democracy against Dictatorship, he has exchanged heated words with protesters.
Thai People Power Party leader Nikhom Boonwiset said Gen Prayut should sit on the unity panel himself, but also said it was a futile effort anyway as it was only a tactic to buy time for the government. Opposition parties also accused the government of not even trying to convince the public it was sincere in seeking unity.