Lawmakers had been expected to vote on setting up a draft reform committee in response to a burgeoning pro-democracy movement that mobilised 30,000 demonstrators last week -- the largest show of force in the kingdom since the 2014 coup.
But the move was delayed when the ruling party proposed a parliamentary committee to further study the six proposed amendments.
Among the more than thousand protesters outside parliament, organiser Tattep "Ford" Ruangprapaikitseree said the government was attempting to "buy time" with the move.
"It shows their insincerity towards the Thai people," he told AFP. "We cannot take it."
Protesters stood on railings to plant pro-democracy stickers high on the closed gates of parliament as guards looked on.
Others spray-painted stencil outlines of a plaque that had been installed during the weekend protest at the historic Sanam Luang park.
The so-called "People's Plaque" was later removed by police. It was meant to reference a plaque commemorating the end of royal absolutism in 1932, which mysteriously vanished three years ago.
King Maha Vajiralongkorn sits at the apex of Thai power, supported by an arch-royalist military and the kingdom's billionaire clans.
The royal family enjoys support from mostly older conservatives, dozens of whom marched to parliament Wednesday to submit a petition with 130,000 signatories against constitutional change.
The ultra-wealthy monarch spends much of his time in Europe, but he was in Bangkok Thursday to mark Prince Mahidol Day, laying a wreath at his grandfather's statue, according to local media.
The movement -- which students claim is leaderless and inspired by Hong Kong's pro-democracy protesters -- is also calling for Prayut Chan-O-Cha, a former army chief who masterminded a 2014 coup, to resign and for the government to stop "harassment" of political opponents.
Online Criticism Scrubbed
Ahead of the protest authorities officially began legal complaints against some of the social media platforms used by the young, tech-savvy demonstrators to further their message.
Action had been initiated against Facebook and Twitter for not complying with a request to take down "offensive" material, said Minister of Digital Economy and Society Buddhipongse Punnakunta.
Last month, Facebook complied with a government request to remove "Royalist Marketplace", a group set up by an exiled government critic which discusses the monarchy's role in Thai society and had more than a million members.
But some 400 requested URLs remain on the platform, said Buddhipongse, declining to say if they had been flagged by his ministry because they criticised the king.
"It's not only politics -- we have other factors covered in the (Computer Crimes Act)," he told AFP.
Facebook declined to comment on the move, while Twitter did not respond.
Thailand's monarchy is protected by one of the world's toughest royal defamation laws but some activists are calling for these to repealed too.
As the lawmakers debated, rally organiser Siraphop Attohi -- also known as "Raptor" -- made a speech from the back of a truck outside parliament, calling for those inside to bring about a constitutional "limit" on the monarchy's power.
"If they still resist... then in the end they would not be able to withstand the people's tide."