Thai Prime Minister Thaksin Shinawatra has offered a concession to his critics by saying he might hold a referendum to amend the constitution.
Mr Thaksin is facing regular protests calling for his resignation
"I welcome the call for constitutional changes, but I have to ask for the public's approval," Mr Thaksin said.
His made the comments in a weekly radio address, shortly before a rally by protesters calling for his resignation.
By late afternoon about 5,000 people had gathered at Bangkok's Royal Plaza, chanting anti-Thaksin slogans.
The prime minister has refused to quit, despite repeated rallies calling for him to go.
A protest last Saturday drew at least 50,000 people - the largest since Mr Thaksin came to power in 2001.
Many of the demonstrators are supporters of media tycoon Sondhi Limthongkul, who has held regular rallies accusing Mr Thaksin of corruption and abuse of power, as well as cracking down on press freedom.
Shin Corp deal
The anti-Thaksin campaign was given recent momentum by his family's $1.9bn sale of telecoms giant Shin Corp.
The deal was heavily criticised in the Thai press, mainly because it was engineered so Mr Thaksin's children - not the prime minister - sold the shares, and the family avoided paying capital gains tax.
Others objected to the deal because they said important Thai assets were being sold to foreigners.
"I think our prime minister is not honest. He sold our assets, our satellites and mobile phones, to Singapore. His action is stupid, and he's not sincere," one protester at Saturday's rally, Dananat Nimitanya, told the French news agency AFP.
Although Mr Thaksin has lost the support of many among the middle classes, he still enjoys considerable support in rural Thailand.
The rally is due to continue until late into Saturday evening, and analysts are anxiously watching the turnout, seeing it as an indication of whether the anti-government campaign is gathering pace or losing momentum.