The Move Forward Party (MFP) is trying to convince senators to back its leader Pita Limjaroenrat to become prime minister as it bids to gather support from other parties to form a coalition government.
The party has been critical of the coup-appointed Senate and sought to "switch off "or remove its power in joining MPs to select a prime minister as stipulated by the constitution.
But it has now made an about-face and has to seek the Senate's backing.
When a joint sitting of the House of Representatives and the Senate is convened to elect a prime minister, under the 2017 constitution, at least 376 votes would be needed for his endorsement.
This means Mr Pita would need more votes from other parties or senators.
MFP secretary-general Chaithawat Tulathon said the party is ready to meet senators for talks to allay any concerns they may have.
"Senators' concerns may be unfounded. If we can talk, they should be eased," Mr Chaithawat said.
"I am confident there are some senators who are mature enough and wouldn't want to see a political impasse,'' he said.
Some senators previously expressed concern about the MFP's desire to revise or scrap Section 112 of the charter, the lese majeste law.
Asked who would become the House Speaker, Mr Chaithawat said the role should be filled by a member of the MFP as it won the most House seats.
Asked whether it has approached the Chartthaipattana Party to join a coalition, Mr Chaithawat said Mr Pita on Monday announced a plan to form a coalition government comprising five former opposition parties and one new party, with a combined 310 MPs and himself as prime minister.
The six parties are the MFP, Pheu Thai, Thai Sang Thai, Prachachart, Seri Ruam Thai and the Fair Party.
A source said Mr Chaithawat will today meet key figures from these parties to discuss the formation of a coalition government.
On Facebook, Srettha Thavisin, a Pheu Thai candidate for prime minister, on Tuesday called on other parties, particularly the Bhumjaithai Party and the Democrats, to support Mr Pita for prime minister without the need for the support of senators.
Mr Srettha noted that he hoped all parties would respect the public mandate by voting for Mr Pita.
"I, for one, support Mr Pita of the Move Forward Party to take the position with grace," he wrote.
He noted that many parties, particularly Bhumjaithai and the Democrats, previously announced their opposition to the 2017 constitution's empowering of senators to take part in the vote for prime minister.
"Now it's time for you to confirm your stance by voting for Mr Pita to be the 30th prime minister in a true democracy, without having to rely on votes from the 250 senators," he added.
Responding to Mr Pita's calls for other parties' support, former House speaker Chuan Leekpai said: "Don't expect others to think the same way. Each party can think for itself."
Deputy Prime Minister Wissanu Krea-ngam said a new coalition government could be formed on the basis of mutual respect and courteous negotiations.
"Any wish can come true when generosity is offered in exchange," he added.
"The formation of the new government is now the burden of the Move Forward Party, which won the highest number of House seats," he said.
The senators are entitled to their own points of view, but their positions should be negotiable, he said.
He said the Election Commission would verify the election results within two months, after which the House will be called into session and the parliament president appointed.