Deputy Prime Minister Chalerm Yubamrung yesterday said the prime minister had ordered him to extend an invitation to the Democrat leader and the party's southern MPs to attend a meeting on the unrest.
He has agreed to chair the meeting next Tuesday at Government House.
He also asked Deputy Prime Minister in charge of security affairs Yutthasak Sasiprapa to invite commanders of the armed forces, the Internal Security Operations Command (Isoc) and the chief of the Southern Border Provinces Administration Organisation to attend.
Earlier, Mr Chalerm issued a personal invitation to Mr Abhisit to attend a discussion on ways to solve the unrest, but the Democrat leader rejected it.
He said he would not take part in the meeting unless Ms Yingluck also attended, because she has "decision-making authority".
Mr Abhisit said he had yet to receive any formal invitation from the government regarding the forum but in principle he would have no problem attending.
Mr Chalerm said the 93 men facing separatist-related charges who surrendered to authorities on Tuesday would have no choice but prosecution if they are accused of criminal offences.
"We have to also care about the feelings of the families of the victims of the southern violence," he said.
However, he saw no problem with the government arranging legal representation for suspects charged with crimes under Section 21 of the emergency decree, Mr Chalerm said.
He stressed this was his own idea and he was not going to formally propose it to Justice Minister Pol Gen Pracha Promnok.
Several more groups of insurgents especially those operating in Songkhla province had contacted authorities through their relatives saying they wanted to surrender, an intelligence officer working in the southern border provinces said.
Fourth Army commander Udomchai Thammasarorach said his meeting with the 93 rebel defectors in Narathiwat on Tuesday should be regarded not as negotiations but peace talks that were part of the work of the Isoc Region 4.
Lt Gen Udomchai said he had explained to the 93 men during the meeting that the army would assist the ones facing criminal charges to enter the justice process.
As for those who were arrested under the emergency decree, the army would decide what to do with them, said Lt Gen Udomchai, adding that he was also trying to propose an end to the decree in the far South.
When the decree is lifted, more people facing charges under this law would probably surrender, he said.
Suspects who have surrendered would now be screened, said Pol Gen Adul Saengsingkaew, the national police chief-designate.