Pita urged senators to remember “we’re all the people’s politicians”.
“My thanks to those that say they’re on the people’s side and siding with the people’s majority,” he said.
Following his speech, Pita told reporters that he had found “closer common ground” with the senators.
“Hopefully, in the four days remaining we will be able to come to a consensus and move this country forward,” he said.
The United Thai Nation Party said last week it was considering whether to put up a rival candidate against Pita.
Caretaker prime minister Prayut Chan-o-cha, who came to power in a 2014 coup and formed a vast coalition government after the 2019 poll, sought re-election under that new party’s banner.
Political analysts say it would be technically possible for him to stay in power under a minority government with support from the Senate.
However, the election results were seen as a national rejection of Prayut and rule by military-linked parties.