The United Thai Nation, Pheu Thai and Move Forward parties have all rejected a suggestion that all parties consider forming a national coalition.
Thanakorn Wangboonkongchana, deputy United Thai Nation Party (UTN) leader, said Senator Jadet Insawang had gone too far.
The Move Forward Party (MFP) won with the highest number of House seats and is still working on the formation of a new coalition, so all sides should respect the party's right to lead this effort, Mr Thanakorn said.
In the event the MFP fails to do this, it will be more suitable to allow the Pheu Thai Party, which has the second-highest number of seats, to try rather than just switch to forming a national government, he said.
The MFP-led alliance has more than 300 House seats and should be supported by all sides in forming a government, Pheu Thai's deputy leader said.
A Pheu Thai MP for Phrae ruled out the possibility of forming a national government, saying the matter should no longer be discussed.
MFP spokesman Rangsiman Rome said he was confident the MFP would form a coalition.
