Deputy Pheu Thai spokesman Jirayu Huangsap said yesterday he had discussed the matter with several Pheu Thai MPs in the North and the Northeast who supported the move.
He said the proposal for the government to form a new investigation panel would be discussed at a party meeting on Tuesday.
The new committee would aim to prove that the TRC was wrong about its findings on the "men in black" and the trajectories of the bullets fired by security forces during the violence, Mr Jirayu said.
In its presentation of the investigation findings, the TRC shed light on the role of the men in black in deadly attacks during the protests, confirming their links to red-shirt figure Maj Gen Khattiya Sawatdiphol, known as Seh Daeng, and the protesters' security guards.
Mr Jirayu also said he had learned from northern and northeastern MPs that the party's voters in at least 20 provinces wanted to send about 10,000 representatives to press for "the truth" from the TRC and the National Human Rights Commission regarding their past probes into the 2010 violence. The two commissions were on the opposite side of democracy, Mr Jirayu said.
Several academics had also criticised the TRC over its findings that had cost about 100 million baht but had not yielded any benefit to society, he said.
Mr Jirayu said he could not believe that TRC chairman Kanit na Nakorn would dare say he saw nothing wrong with the fact that some members of the TRC were from the yellow shirt People's Alliance for Democracy.
That reflected a lack of neutrality and the TRC "should be renamed as a committee to protect Democrat Party leader Abhisit Vejjajiva" and stop talking about its investigation results, Mr Jirayu said.
Former prime minister Somchai Wongsawat said he was puzzled by the TRC's recommendation that ousted prime minister Thaksin Shinawatra end his political role for the sake of national reconciliation.
Mr Somchai, a brother-in-law of Thaksin, said he doubted if such a recommendation was right as Thaksin had done a lot for the country and that was why he had a large number of supporters.
The people behind the 2006 military coup should be the ones to apologise to the public. As for Thaksin, he would surely return to Thailand one day because many people wanted him to do so, Mr Somchai said at a Pheu Thai seminar yesterday.
The seminar was held to launch a new book, The Truth for Justice, that is published by the People's Information Centre, a group focusing on information regarding the victims of the 2010 violence.
At the seminar, copies of two letters composed by Thaksin were also released. In one letter intended for people who lost their loved ones during the political violence between April and May, 2010, Thaksin concluded that the dispersal of the protesters carried out under the Abhisit Vejajiva government had resulted in the highest casualties ever.
In the other letter, Thaksin thanked people whom he described as heroes for their sacrifice and fight for democracy.
Meanwhile, Mr Abhisit said his party's legal team was working on Department of Special Investigation chief Tarit Pengdith's allegation that he and former prime minister Suthep Thaugsuban intended to kill people by ordering the security forces to reclaim areas from the red shirt protesters.