Pheu Thai's support for amendments to the lese majeste law was welcomed by the Move Forward Party on Monday, but Democrat leaders opposed any change.
Pheu Thai's new policy was announced on Sunday, after its general assembly and election of a new leader.
Rangsiman Rome, deputy secretary general of Move Forward, welcomed the Pheu Thai announcement. He said MPs could now push ahead with proposed amendments in the House of Assembly.
Pheu Thai under the new look of younger leader Nan MP Chonlanan Srikaew announced on Sunday its support for the amendment of Section 112, known as the lese majeste law, because it was being abused by people in power to subvert justice.
The amendment would open authorities involved in the justice process to examination whether they acted in the line of duty and within the intention of the law.
"As the party with the most MPs in parliament, the Pheu Thai Party stands ready to push for the amendment to be placed on the agenda of the House meetings," Chaikasem Nitisiri, the party's chief strategist and a key legal adviser, said.
Pheu Thai announced it position on Sunday as anti-government protesters rallied against the lese majeste law at Ratchaprasong intersection in downtown Bangkok. The Pheu Thai statement came with the #Mob31Oct64 hashtag, one used by the demonstrators.
Pheu Thai also promised to push for the amendment of the Computer Crimes Act, for the same reasons. (continues below)
Protesters led by the United Front for Thammasat and Demonstration organised a rally at Ratchaprasong intersection on Sunday to collect signatures for another bid to end the lese majeste law. (Video by Jetjaras Na Ranong)
Thammasat University student activist Panusaya “Rung” Sithijirawattanakul said on Sunday the protest organisers collected signatures calling for an end to the lese majeste law, in addition to their demand that all detained protesters to be released.
Ms Panusaya did not mention this issue when she joined Amnesty Thailand on Monday in delivering a petition addressed to Prime Minister Prayut Chan-o-cha at Government House calling for an end to violations of the rights of people who hold opinions that differ with the government's.
Democrat Party leader Jurin Laksanawisit said Thailand's oldest party (a member of the government coalition) had no desire to touch Section 112, because the constitutional monarchy was the most suitable for the country.
"The party's ideology is not dictated by situations or driven by political moves," he said.
Deputy Prime Minister Wisanu Krea-ngam said political parties can push for the amendment through the parliamentary process, with no need for endorsement by the government.
Parliament does not need to meet behind closed doors when the matter comes up for debate, he added.