The Thaksin Shinawatra-backed Pheu Thai Party is preparing to field candidates for Speaker and said it should be given the chance to form a government.
Pheu Thai had an executive meeting on Wednesday to discuss its parliamentary prospects and agreed to run for house Speaker and the deputy positions.
If the pro-junta Phalang Pracharat Party led a coalition with the support of more than 15 parties, Democrat Banyat Banthathan reportedly would become the house Speaker.
But Banyat rejected the offer on Tuesday, saying he would be more useful as an ordinary MP.
Pheu Thai, after the executive meeting, issued internal letters to MPs and members to comment on the nomination by 6pm on Friday before a vote on Saturday, one day after the Parliament opens.
Pheu Thai secretary-general Phumtham Wechayachai said the party remained firm in its intention to form a coalition.
It was ready to enter talks with any party and compromise on its political positions to end the crisis, Phumtham added.
The key parties, Democrat and Bhumjaithai, are yet to make an announcement about which bloc they will support.
But Phumtham said there should be clarity about the establishment of the government before Saturday.
As the party with the most lower house seats, it had the right to form a government, he said.
Any attempt to bypass Pheu Thai to form a coalition was inappropriate and the party would oppose it, he added.
Phumtham called on the Democrats and Bhumjaithai, which had 103 MPs in total, to take a responsible position to break the deadlock.
He said voters would decide whether the parties were acting in the public interest.