BANGKOK, July 21 (Reuters) - Thailand's election-winning Move Forward party announced on Friday it was making way for runner-up Pheu Thai to try to he form the next government, after its leader's bid was twice thwarted this month by a military-backed Senate.

The progressive Move Forward and populist Pheu Thai have the lion's share of lower house seats after trouncing conservative, army backed rivals in a May 14 election, in what was a clear rejection of nine years of military-backed rule.

The two parties are part of an eight-party alliance that had backed Move Forward's leader, U.S.-educated liberal Pita Limjaroenrat, for the premiership, before conservative opponents and Senators blocked him in a July 13 parliamentary vote, and again stifling his re-nomination six days later.

Pita's ambitions to be Thailand's next leader were also dented by the Constitutional Court accepting two cases against him in the space of a week, including a temporary suspension as a lawmaker for his alleged violation of election rules, which he denies.

"It is clear that conservative forces - from politicians, business monopolies and institutions - they will not let Move Forward become government," party secretary Chaithawat Tulathon told a press conference.

"The important issue today is not if Pita can be prime minister but returning democracy to Thailand ... we will give the opportunity for the country and let the second placed party form a government."

Pita told Reuters on Tuesday he suspected there would be "pre-planned" obstacles.

Move Forward and Pheu Thai have 151 and 141 seats in 500-member lower house, respectively, but their alliance needs the backing of more than half of the combined chambers, including a 249-member Senate appointed by the military after a 2014 coup, which has voted as a bloc to protect establishment interests.

Move Forward's ambitious agenda of ending business monopolies and reforming the military and a tough law that insulates the monarchy from public criticism, represents a challenge to conservatives and old money elites, which have for decades wielded influence over Thailand's politics.

Chaithawat said rival lawmakers had used Move Forward's bid to amend article 112 of the criminal code, which prohibits insults of the crown, as a pretext to deny the will of the people.

"They used 112 as an excuse and used loyalty (to the monarchy) to clash with the public vote," he said.

Pheu Thai, the political juggernaut of the billionaire Shinawatra family and Thailand's most dominant party for two decades, is expected to nominate real estate mogul and political newcomer Srettha Thavisin for prime minister for the next vote on July 27.

The benchmark Thai index (.SETI) and baht were both up slightly in Friday morning trade.

Pheu Thai faces the many of the same hurdles as Move Forward, and has its own bitter history with the military, which overthrew two of its governments, leading to criminal charges that forced two prime ministers - siblings Thaksin Shinawatra and Yingluck Shinawatra - into self-imposed exile.

But it has been more circumspect on the proposal to amend the royal insult law.