Pichet, who is a Pheu Thai MP for Chiang Rai, told reporters on Thursday that he had scheduled the first vote for a new prime minister on July 13.
If Pita does not receive sufficient votes, a second round will take place on July 19 and, if necessary, a third round on July 20, he said.
The Constitution does not restrict the number of times a PM candidate can be put forward for a vote.
Pichet was adamant the eight parties of the Move Forward-led coalition would stick together when voting for a PM, as per the memorandum of understanding they signed following the May 14 election.
Asked about some senators’ declaration that they would not vote for Pita, Pichet said he was unsure how many senators would back the Move Forward leader, but he believed many of them want the next government to be formed successfully.
Senator Prapan Koonmee told media on Thursday that he and other senators would not vote for Pita owning to his political stance as they believe his party’s ambition to amend the lese majeste law threatens the constitutional monarchy.
Pita also faces several legal challenges in his bid to become the country’s next leader.
To be elected as prime minister, he needs a simple majority of at least 376 votes from a combined vote by the 250-member Senate and the 500-member House.