"However, we must remember that 24 Red Shirt leaders are facing arrest and there’s no mention of those charges being dropped so there’s a lot of water under the bridge."
Police with riot gear and armed soldiers remained deployed near the protest site on Monday, but there was no immediate sign of increased security or preparations for action.
"Even in the last few hours, there was still talk coming out of the government of some sort of force being used to get rid of these protesters which means there are definitely two different kinds of scenarios here," our correspondent said.
Abhisit's offer follows Sunday's emergency cabinet meeting that tried to resolve the long-running standoff with the protesters.
Panitan Wattanayagorn, the government's spokesman, said the meeting addressed the grievances of the red shirts although he added that high on the agenda was "poverty".
The red shirts have barricaded roads and closed down several parts of the capital in crippling protests that have threatened to suck in pro-government activists called the "Yellow shirts".
The protesters are calling for parliament to be dissolved within 30 days or less while an election must be held within 60 days of parliament being dissolved.
At least 27 people have been killed and nearly 1,000 wounded in ensuing violence between the protesters and security forces.
The red shirts, mostly from the rural and urban poor, view the government as an illegitimate puppet of Bangkok's elite and the military.
They say it came to power through behind-the-scenes parliamentary manoeuvring after a court decision that disbanded the ruling party aligned with Thaksin Shinawatra, the former prime minister who was ousted in a 2006 military coup.