BANGKOK, May 18 (Reuters) - The leader of the progressive Move Forward Party that secured a stunning victory in Thailand's election this week said on Thursday he was confident of building more support and being able form a stable and balanced government.

Speaking at a press conference as part of an alliance of eight parties with about 313 of the 500 lower house seats, leader Pita Limjaroenrat said there was a team in place to muster support to ensure the alliance could secure enough seats to rule.

"There is a committee and negotiation team in place to find out what I further need, the seats I need, so there is stability and no loss of balance in governing," he said.

He added: "My coalition is taking shape. And we have a very clear roadmap from today and until the day I become PM."

Pita and his allies say they have a mandate from the electorate to end nearly a decade of conservative, army-backed rule in Southeast Asia's second-largest economy.

The alliance overnight added two more members and three seats but it still appears short of the 376 votes needed from the 750-member bicameral legislature to vote in a prime minister to form a government.

The challenge for the alliance is winning votes from the 250 members of the upper house Senate, a chamber that was appointed by a junta after a 2014 coup and has a record of siding with army-backed parties.

Those parties were thrashed in Sunday's election by Move Forward and the populist heavyweight Pheu Thai, but the prospect of a pro-military bloc forming a minority government - assuming they have the Senate's support - cannot be ruled out.

Pita's alliance was dealt a blow late on Wednesday when Bhumjaithai, the third-place finisher with a projected 70 seats, indicated it would not back any prime minister who supports amending or abolishing a law against insulting the monarchy.

Move Forward has campaigned on changing the lese-majeste law, under which at least 200 people have been charged in the past few years, many from a youth-led protest movement. The law prescribes jail terms of up to 15 years for each perceived offence, with some given sentences of several decades.

Asked about that, Pita said: "That is their matter. The eight parties have a position and clarity."

He also said he was not concerned about any pending cases filed with the election commission seeking to disqualify him over shares he allegedly held in a media company.

"I'm not worried ... I understand there are many dimensions in politics," he said. "As a public figure I can accept the investigation."