Pita is the leader of the Move Forward Party and its sole prime ministerial candidate.
The vote has been scheduled for next Thursday, with subsequent rounds of voting expected on July 19 and 20.
Pita should be given a “second chance” if he fails to secure majority support from both Houses in the first round of voting, said Srettha, a former property tycoon turned politician.
But he also said that the actual vote result should be taken into account.
He also confirmed Pheu Thai’s “full support” for Pita to become Thailand’s 30th prime minister.
“We already cast the ballots. The general election was already over. Now we want to see the vote to get a new prime minister on July 13 go smoothly. I can confirm that Pheu Thai MPs will vote in line with the party resolution to support Pita as Thailand’s 30th prime minister,” Srettha said.
He noted that Pita himself was confident of getting enough support from both Houses of Parliament. Srettha was speaking on the sidelines of a panel discussion at the Bangkok Marriott Marquis Queen's Park Hotel.
Earlier, there were calls from political parties outside of the eight-party coalition led by Move Forward for Pheu Thai, the second-largest coalition partner, to nominate its PM candidate for the parliamentary vote if Pita failed to get the required number of votes.
In the May 14 general election, Move Forward won the largest number of MP seats – 151 out of 500 up for grabs – followed by Pheu Thai, with 141 MP seats.
Pita has been reassured of support from 312 MPs in the coalition, but he still needs at least 64 more votes of support to get the parliamentary endorsement to become prime minister.
A provisional clause in the Constitution empowers the 250-member Senate to join the 500-member House of Representatives in selecting the prime minister. Anyone nominated for the PM seat requires majority support from both Houses, which is 376.
Many senators said they would not vote for Pita as his party sought amendments to Article 112 of the Penal Code involving lese majeste, which they said would weaken Thailand’s monarchy and undermine the country’s security.