Thailand's military-installed government offered to negotiate with ousted Prime Minister Thaksin Shinawatra, as thousands of protesters support the former leader.
The demonstrators, however, said they postponed a planned march to military headquarters, fearing possible violence. Both the protesters and military have accused each other of planning to provoke clashes.
They said they had received a tip that the military would spark a confrontation as an excuse to arrest protest leaders.
"We decided not to march tonight because we are afraid that we will fall into a trap," said protest leader Jakrapob Penkair. He said supporters instead would march Sunday morning to military headquarters to demand that coup leader Gen. Sonthi Boonyaratglin resign.
Police estimated about 10,000 joined the rally at Sanam Luang, an open park near Bangkok's Grand Palace. Huge posters of Thaksin were erected at the rally site, along with signs demanding the military-installed government step down.
Though it went off peacefully, the military warned earlier in the day that Thaksin supporters would turn to violence.
"The officials are trying to use the most lenient approach to deal with protesters," said Lt. Gen. Prayut Chan-ocha, army chief for the central region, which includes Bangkok. "However, the protesters are trying to provoke violence. We should condemn such acts."
He said military intelligence had information the protesters had gathered clothing, bottles and gasoline materials that could be used to make petrol bombs.
On Friday night, an estimated 13,000 supporters gathered at the same park to hear Thaksin attack coup leaders in a video message from London, where he has been living in exile since last September's coup.
Thaksin denounced the government's decision to freeze bank accounts belonging to him and his family containing more than 52 billion baht (US$1.6 billion; EUR1.2 billion) because of suspicion the money might have been obtained by corruption.
"I will fight for my honor to prove my innocence," he said. The crowd erupted into cheers of "Thaksin, fight, fight!"
Prime Minister Surayud Chulanont responded Saturday, saying that Thaksin was welcome to return to the country and that coup leaders wanted to talk with him.
"I am ready to negotiate," Surayud said in an interview with a government-owned television station. "An important issue which Thaksin wants to negotiate will be about his assets and family."
Earlier Saturday, about 3,000 people gathered at the Royal Palace in what was billed as a peace rally, according to the Bangkok Post newspaper's Web site. Singing the national anthem, the participants called on Thaksin supporters to respect the rule of law.
"We want those protesters to gather peacefully and sympathize with the majority of the people who want to see the country in order," Air Chief Marshall Bannawit Kengrien, a National Legislative Assembly member, told reporters.
In his video message, Thaksin decried restrictions on politics and civil liberties imposed since the coup, calling for the restoration of democracy. Last month, a court ordered his Thai Rak Thai party dissolved for election law violations and barred its entire leadership of 111 people, including Thaksin, from public office for five years.
"I already said that I'm retiring from politics, but I am just asking that my family and I live with dignity," Thaksin said.
The anti-government protests, while slowly growing in size and enthusiasm, have so far failed to have a significant impact on political affairs.
They have, however, contributed to a sense of uneasiness that the risk of confrontation is growing between Thaksin's supporters and those who overthrew him for alleged corruption and abuse of power.
The government has issued repeated warnings about potential violence, and urged people to ignore rumors of another coup.