After a meeting with the alliance, Pita said his re-nomination for prime minister could not be blocked by the Senate.
However, Pita added that if he failed again he would let Move Forward's ally, the Pheu Thai party, "take action".
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.
Persons:
Wednesday Pita, Pita Limjaroenrat, Pita, Pheu Thai, Srettha Thavisin, Orathai Sriring, Panarat, Kanupriya Kapoor, Alex Richardson
Organizations:
Wednesday, Senate, Constitutional, Thomson
Locations:
BANGKOK, Thailand's, Thai, May's, Pita