Jatuporn Prompan, one of the three protest leaders involved in the negotiations, said they would return to the table on Monday, but pressed the prime minister to meet their request within a fortnight.
"We ask you to dissolve the house within two weeks. Whatever your decision should be, if we talk tomorrow, I want you to consider this condition," Jatuporn told Abhisit.
Abhisit smiled and promptly concluded the talks, saying: "I don't think we need to have ultimatums or deadlines."
The debate, aimed at ending protests by the red shirts who have massed for weeks in the Thai capital Bangkok, took place at an educational institute and was broadcast live on television.
Al Jazeera's Aela Callan, reporting from Bangkok, said the decision to televise the debate served several purposes.
"One was that the prime minister could show that talks were going on, and two was in the spirit of keeping things open ... however it has become a largely unsuccessful evening for both parties," she said.
"The government has emerged without assurances that the red shirted protesters will leave the street, and likewise the protesters have had no assurances that the government is even considering its demands to dissolve parliament and call fresh elections."
Thousands of protesters watched the talks on a large screen at their rally ground in Bangkok's government quarter, waving their signature plastic clappers as their leaders spoke.
The protests started on March 12 have turned increasingly confrontational and raised fears of violence.
On Saturday, they forced soldiers across Bankok to pull back from temporary postsset up to police the mass demonstrations over the previous weeks.
But the protests were marred by a series of explosions that injured four soldiers and several civilians.
The red shirts are mainly supporters of Thaksin Shinawatra, a former prime minister who was deposed in a 2006 coup and who now lives in exile to avoid a jail sentence for corruption.
The protesters say Abhisit took power illegitimately.
Thaksin regularly addresses his supporters via videolink, raising the prospect of a campaign of civil disobedience if Abhisit continues to refuse their demands.