Video broadcasts from the protests showed a large number of people being helped or carried away from the site after water cannons and tear gas was sacked at them, but there were no reports of serious injuries.
The wounded included one royalist supporter shot in the hip and a pro-democracy protester hit in the leg, police said.
Protesters use inflatable rubber ducks as shields to protect themselves from water cannons, outside the Parliament in Bangkok, Thailand, on November 17, 2020.
The planned venue of Wednesday's protest, the Rajprasong intersection in the middle of the city's upmarket shopping district, is just minutes away from the national police headquarters. The protest movement has been staging increasingly determined mass rallies of thousands of people around the country.
The charter allows the military-appointed Senate, whose powers protesters want scrapped, to vote for the premier. Constitutional changes require a joint vote of those two bodies. Any that are passed will have to go through second and third votes after at least a month.
Lawmakers adjourned a previous session without voting on proposed amendments, leading the protesters to accuse the government of bad faith.
The kingdom has been rocked by months of student-led protests demanding changes to the military-scripted constitution and the removal of Prime Minister Prayuth Chan-ocha, who first took power in a 2014 coup.
"We will not touch on that", said Wirat Ratanaset of the ruling coalition.
Protesters also want reforms in the Thai Senate, where members are now not elected into office. It is protected by a law that makes defaming the monarch punishable by up to 15 years in prison.
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Police set up barricades outside the Parliament, where hundreds of royalists earlier demonstrated to call on MPs not to change the constitution.
Fearing trouble, many protesters came equipped with helmets, goggles and gas masks, but after the impromptu paint job, they dispersed peacefully.
More than 50 people were injured, mostly by tear gas, according to an ambulance and medical coordination service, which said six people were shot. No further details were available.
There were reports of at least six people being shot as police said they did not open fire with live ammunition or rubber bullets. Late Tuesday prominent student leader Parit "Penguin" Chiwarak said a "new era" in the movement had begun. Some lawmakers had already left the scene by boat from a pier behind Parliament.
The government has tried to assuage protesters' anger by signaling willingness to compromise on the constitution and find a solution to the crisis, putting the parliament under pressure to back the amendments. The protesters back a proposal that would roll back aspects of the current 2017 constitution - enacted during military rule - that granted extra powers to unelected branches of government, such as the Senate.
Instead, Parliament is likely to establish a drafting committee to write a new charter.
"Without the people, the government and monarchy will have no power", said Panusaya Sithijirawattanakul, one of the protest leaders.
The monarchy is a virtually untouchable institution that the royalist establishment and many ordinary citizens consider to be the heart and soul of the nation, and the motion had not been expected to pass.