It had racked up more than 7.6 million votes with more than 90 percent of ballots tallied, giving any government it tries to form a claim to legitimacy. But Pheu Thai argues it has won the most number of MP seats and therefore should be invited first to form the government.
Future Forward, a new party popular among young people, had almost 4.8 million.
As Thai voters select their next government in the wake of nearly five years of direct military rule, critics have slammed the voting system, accusing the junta of rigging results to favor pro-military political groups.
The pro-army Palang Pracharat party said earlier on Monday it aims to form a government "after winning the most votes", Reuters reports.
But however the numbers play out, coup leader Prayut's party will benefit from a military-appointed 250-member Senate, meaning it only needs 126 lower house seats - compared to 376 for Pheu Thai.
Despite that, analysts had not expected the army-linked Phalang Pracharat party to win the popular vote, given mounting anger at junta rule and the enduring popularity of Pheu Thai - the party of ex-premier Thaksin Shinawatra.
Critics have said a new, junta-written electoral system gives a built-in advantage to pro-military parties and appears created to prevent the Thaksin-linked Pheu Thai Party from returning to power.
One party said it was considering a legal challenge over what it said were poll irregularities and, amid popular dismay over the partial results, the number of signatures on an online petition to impeach the Election Commission leapt by more than 300,000 over a few hours to more than half a million. "But I do wish that the party that we will get, the party that wins the votes, will come in and improve our country".
"If you look at the number of ballots and the number of voter turnout, the ballots much more exceed the number of voter turnout in many, many provinces", he said.
Prayuth was among the first to vote in Bangkok, the capital, arriving in a black Mercedes after polling booths opened at 8 a.m.
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An electoral staff member shows a ballot during vote counting at the general election in Mae Hong Son, Thailand March 24, 2019.
"We will ensure that we will do everything according to the mandate of the voters who want us to move the country forward peacefully", he said.
This was followed by the military-backed Palang Pracharath party with 97 seats. His sister, Yingluck Shinawatra, who led the government that was ousted in 2014, also fled the country after what supporters said was a politically motivated corruption prosecution.
A statement from Prayuth's office said he thanked people for voting and officials for holding the election in an orderly fashion.
"As long as we still have breath, we can not give up", he said in a Facebook post on today. The Election Commission announced the results of 350 constituency races but full vote counts, which are needed to determine the allocation of 150 other seats in the House of Representatives, won't be available until Friday. "It will be clearer once the official result is announced", he said.
Questions are also being raised about the credibility of the vote and the next administration is likely to be unstable, Thanathorn Juangroongruangkit, the head of Future Forward, said in a television interview on Monday.
"I feel very excited because we haven't had an election for many years". While the Democrats promised not to join with any military proxy the party leadership said it does not speak for all democrats and we may see some defections to a military coalition.
Another royal command torpedoed the candidacy of his elder sister Princess Ubolratana for prime minister of a party linked to Thaksin, a divisive ex-premier toppled by a 2006 coup.
The kingdom remains bitterly divided despite the ruling junta's pledge to rescue it from a decade-long treadmill of political instability, protests and coups.