A group of Pheu Thai Party supporters on Sunday urged it to let the Move Forward Party form a coalition government without its help, expressing frustration against "disrespect" shown towards Pheu Thai.
The Pheu Thai leader said he would take the group's opinion into consideration.
A group of red-clad supporters showed up at Pheu Thai's headquarters to express their views.
Leading the group, Niyom Nopparat said they wanted Pheu Thai to withdraw from the Move Forward Party's effort to form a coalition government because Pheu Thai had been "disrespected" in the process.
"The Pheu Thai fanclub wants to urge parties to think carefully if a government can be formed without the Pheu Thai Party," he said.
The group's appeal came as Pheu Thai and Move Forward were arguing over the House Speaker's position.
In its statement, the group wanted Pheu Thai to let Move Forward, as the election winner, try to form a government first. If Move Forward fails to do so, Pheu Thai would take its turn because it won the second most House seats.
Meanwhile, Pheu Thai leader Cholnan Srikaew said the party would carefully consider the group's proposal.
"The party is listening to opinions from all parties, especially from supporters who the Pheu Thai Party must value," Dr Cholnan said.
The Pheu Thai leader said Move Forward would have a meeting with coalition allies on Tuesday and he expected they could agree on the identity of the House Speaker.
"We must find the most promising conditions for our collaboration... There must be give and take. There cannot be a total winner or loser. Then everyone will be happy," Dr Cholnan said.