Monks and elephants walked in searing heat to the parliament
They were joined by more than 1,000 supporters who also want Buddhism to be declared the national religion in the new post-coup constitution.
The leaders behind last September's coup have indicated they may be willing to bow to the monks' demands.
Critics fear it could inflame tensions in the Muslim-majority deep south.
In the south a three-year Islamic insurgency - in a country where 95% of the population are Buddhist - has killed more than 2,000 people.
Constitution 'review'
Correspondents described a colourful procession as monks dressed in saffron-robes walked alongside the nine elephants 30km (18 miles) from Bangkok's western suburbs to parliament.
Police had asked the protesters not to bring the elephants for fear the scorching heat would make them difficult to control, but they relented as the march continued into the city.
"Our only demand is to have the clause 'Buddhism is Thailand's national religion' included in the new constitution. It's the opinion of the majority of Thais," protest spokesman Tongkhao Phuangrodpang told the AFP news agency.
Coup leader and army commander General Sonthi Boonyaratglin said he expected the committee drafting the constitution to "review its decision on this issue".
"If a stipulation in the charter to this effect leads to peace in the country, then it is better that it is included," he was quoted by the Bangkok Post as saying.
"Those who say there is no need for such a stipulation don't take the issue that seriously."
He recommended adding a clause, saying the government will "take care of other religions, including Christianity and Islam".
A draft of the new constitution, released last week, keeps the same wording as previous constitutions - that the state will protect all faiths, with no mention of Buddhism as the national religion.
Thailand's draft constitution has come under fire from Buddhist monks and supporters for not having a clause declaring a national religion for the country.  The coup-appointed Prime Minister, Surayud Chulanont, noted that the issue could cause problems with the upcoming referendum to ratify the proposed constitution.

According to the Bangkok Post 20,000 protesters gathered outside the parliament building in Bangkok, and a procession of nine elephants joined the protest with Senator Sawet Thinnakul riding one of them.

It would appear that the government has carefully worded the draft constitution to avoid favouring one religion over another.  Tensions and violence in the predominantly Malay Muslim south of the country have led to over 2,000 deaths; having a clause that recognised Buddhism as the country's official religion may further inflame tensions in the region.