United Thai Nation (UTN) deputy leader, Suchart Chomklin, has indicated it might benefit the country more if the party's MPs did not vote for a new prime minister by adhering to party wishes.
Mr Suchart said on Tuesday there are steps to be followed prior to the vote.
First, it must be established if the UTN will be included in the new coalition government. The party said it had not been invited by Pheu Thai, which is leading current efforts.
"Let's take one step at a time," he said. "To be honest, I want to see the country move forward."
Mr Suchart, also the labour minister, said the stock market rallied when the news broke of Bhumjaithai, the third-largest party, accepting Pheu Thai's invitation to join the government on Monday.
That development has boosted investor confidence, he added.
Mr Suchart was asked whether the UTN's 36 MPs would vote for a new prime minister in compliance with a party resolution or whether they could cast their votes freely.
"If obeying the party line was damaging to the country, would you do it?
"As MPs, we need to consider the course of action we take. If it's bound to provoke conflict and cause a stalemate in the country, we must talk this out in the party," he said.
Mr Suchart said party MPs should think carefully about whether exercising their privilege in voting for a prime ministerial candidate will benefit the country.
In the next prime ministerial selection round in parliament, Pheu Thai is poised to nominate Srettha Thavisin.
Mr Suchart, who leads a 5-9 MP faction in the UTN, said he was staying put in the UTN despite growing speculation he might defect in the wake of Prime Minister Prayut Chan-o-cha's decision to step away from the party.
Gen Prayut has quit as a UTN member and its chief adviser, a move apparently aimed at enabling the party to ease its way into a Pheu Thai-led government if it was offered a place.
Pheu Thai appears reluctant to include "uncles' parties" in the new line-up, referring to the UTN formerly linked to Gen Prayut and the Palang Pracharath Party led by Deputy Prime Minister Prawit Wongsuwon.
Pheu Thai declared during the election campaign it would not form a government with either party, a result of the 2014 coup that toppled the Pheu Thai-led administration.
Thanakorn Wangboonkongchana, another UTN deputy leader, said Gen Prayut had washed his hands of the party. "There isn't an uncle in the UTN anymore," he added.
The issue of Gen Prayut running the show openly or from behind the scenes should be laid to rest, he said, adding it should not be cited as a precondition when forming a government.
He said all parties should be open to talks.