"If talks can bring peace to the country, I am ready to meet him anywhere, because Thaksin is the only person that can end the siege," he said on Wednesday.
But Suthep, who is in charge of the nation's security, rejected Thaksin's demands, saying some of them, such as snap polls, were "impossible".
The government's offer was rejected by Jatuporn Prompan, a leader of the United Front for Democracy against Dictatorship (UDD) group that has been leading the week-long protest to demand Abhisit's resignation.
"The situation now is beyond negotiation," said Jatuporn, whose group accuses Abhisit of being a pawn of the military who ousted Thaksin in a coup in 2006.
"Our objective is to remove them. Why would we talk to them?"
Hundreds of government forces wearing helmets and carrying riot shields stand guard behind coils of barbed wire but police have taken no action against the thousands of red-shirted protesters despite the court order on Tuesday that they allow ministers to enter Government House.
Suthep said the government wanted to avoid violence but has accused the UDD of seeking to provoke a violent incident.
|Government forces have not moved to enforce the court order against protesters [EPA]
UDD leaders have vowed to stay until Abhisit steps down but have promised not to invade Government House or other facilities.
Jatuporn also accused the government of cutting the signal to a television station which has been broadcasting Thaksin's speeches and warned that the move "will only make more people come out".
The protest - the latest escalation in Thailand's three-year-old political crisis - is the largest and longest of several held by the red shirts since Abhisit took office in December after a court decision that removed Thaksin's allies from power.
Economists are worried the latest unrest will hurt efforts to revive an economy hit by falling exports due to the global economic downturn.