Al Jazeera's Marge Ortigas, reporting from Bangkok, said Abhisit was attempting to reconcile all sides of Thai society, and had asked for a constructive exercise, free from criticism and sarcasm.
In the most recent round of protests, Thaksin's supporters and soldiers fought street battles in the capital, Bangkok, that left two people dead and about 130 injured.
The government has extended an emergency law first imposed on April 12, saying that it was still needed amid reports of more protests planned by anti-government demonstrators.
The marathon parliamentary session comes as the country's foreign minister accused Thaksin of being behind last week's attack on Sondhi Limthongkul, who has been at the forefront of a movement against the former premier.
In a speech to the Asia Society in New York on Tuesday, Kasit Piromya accused Thaksin of playing a role in Friday's shooting which left Sondhi injured.
Sondhi founded the Yellow Shirts movement that helped topple Thaksin in 2006 as well as successive pro-Thaksin governments that led to the installation of the current government.
Unidentified assailants riddled Sondhi's car with bullets in Bangkok on Friday, but doctors said he was out of danger after a successful operation to remove a bullet fragment from his skull.
Kasit said Sondhi "was supposed to have lunch with me at noon, but he was shot before".
"It's been survival for a few of us ... Thaksin failed on the populist movement and now I think he has resorted to some sort of assassination attempt," he added.