"It's tricky for them. They have to do it in a way that does not embarrass the leaders and disappoint participants too much because that could undermine their credibility among their own supporters," said political scientist Somjai Phagaphasvivat.
"But it would help their image, especially among the public who are on the fence -- people who agree with their cause but have been reluctant to join because they do not support Thaksin and disagree with violence."
Asked if he was ready to talk to the protesters, Abhisit told reporters before leaving to look at drought problems in the north: "If they want to exchange ideas ... I am willing to listen, but I have to decide on the basis of the whole country."
Deputy Prime Minister Suthep Thaugsuban said the government remained vigilant as it continued to receive intelligence that there could be sabotage, including bombings and arson. Critics have accused the government of scaremongering.
Allies of Thaksin, hugely popular in the vote-rich north and northeast, are likely to win the next election, which must called by the end of 2011, just as they have every poll held since 2001. (Additional reporting by Chalathip Thirasoontrakul and Ploy Ten Kate; Editing by Alan Raybould and Bill Tarrant)