Pita, leader of the progressive Move Forward party - the surprise winner of a May 14 election - failed in his initial bid to win the requisite support of more than half of the combined lower house and military-appointed upper house, or Senate.
The legislature will hold another vote on Wednesday.
After a meeting with the alliance, Pita said his re-nomination for prime minister could not be blocked by the Senate.
He also said his candidacy should not be affected by a complaint against him that was filed to the Constitutional Court.
However, Pita added that if he failed again he would let Move Forward's ally, the Pheu Thai party, "take action".
"If there is no substantial improvement, I have to think about this country... I'll step aside and let the second party try to be the manager of the next cabinet," 42-year-old Pita told reporters.
At the weekend, he raised the prospect of a political ally leading the new government if he failed to become prime minister.
Pheu Thai won the second-largest share of votes in May's election. One of its prime ministerial candidates, real estate magnate Srettha Thavisin, could be nominated for the next leader in the third vote for prime minister, if any.
In last week's vote, Pita secured 324 votes, with only 13 senators backing him and the rest voting against him or abstaining, which his party said indicated some were acting under duress.
Pita, a liberal from the private sector, has won huge youth support for his plan to shake up politics and bring reforms to sectors and institutions long considered untouchable.
That includes a law that prohibits insulting the monarchy -by far Move Forward's most contentious policy and a big obstacle in its attempts to persuade legislators to back Pita.