The Move Forward Party (MFP) submitted a proposal to parliament on Friday seeking to strip the military-appointed senators of their power to co-select the prime minister.
The move to revoke Section 272 of the charter, which allows the 250-member Senate to join the process of selection a prime minister, came a day after the party's leader Pita Limjaroenrat failed to muster enough support to back his bid to land the job. It is the seventh attempt to strip the Senate of this power to date.
MFP secretary-general Chaithawat Tulathon said the party's MPs have all signed in support of amending the charter to strip the Senate of this power because the senators opted to abstain from voting this week.
He said 156 senators abstained while 43 others did not attend the meeting on July 13 to select the nation's new prime minister.
"As the senators clearly expressed that they didn't want to exercise their [voting] rights, we are proposing a solution. We believe it will be a way out for senators and for our parliamentary system," he said.
He said the MFP was opposed to Section 272 and decided to try changing it again after that vote.
Mr Chaithawat said the party's ally, Pheu Thai, had no objection to the move. He said other parties, including Bhumjaithai and the Democrats, would also support such a charter amendment.
The MFP secretary-general said the proposal could go ahead despite the selection of a new PM not yet being been finalised. He added that it could clear parliament within three weeks of its first reading.
The petition has already been accepted by new parliament president Wan Muhamad Noor Matha, who said the petition would be put on the agenda after it has been examined and verified.
Prasert Chantararuangthong, secretary-general of the Pheu Thai Party, said he doubted the MFP's efforts would bear fruit.
He said the proposal faces a major hurdle because it requires the approval of senators and MPs. At least one-third of senators, or about 84, must give it the nod.
He said those who were opposed to Mr Pita's nomination took aim at the MFP's plan to amend the lese majeste law.