He said the red shirts must also abandon their protests that have brought weeks of chaos and occasional deadly clashes to the Thai capital, Bangkok.
"Everybody can calculate the date," Abhisit said, indicating that parliament will be dissolved between September 15-30.
"If they don't go home, I'm not going to dissolve parliament," added Abhisit in a live interview on ASTV.
"I repeat, I am not negotiating with anybody."
Under the Thai constitution, parliament must be dissolved 45 to 60 days before an election.
The timing of the dissolution has been a crucial issue, and the red shirts rejected Abhisit's earlier offer to dissolve parliament by the end of the year.
Abhisit has said he wants enough time in office to pass a national budget for next year.
But both sides want to be in control when a key reshuffle of top military posts occurs in September.
The red shirts however remain suspicious, and are demanding a specific date before they end the rallies that have paralysed the commercial heart of Bangkok.
Weng Tojirakarn, a red shirt leader, told supporters to remain on their guard, accusing the Abhisit's party of having backtracked on promises in the past.
"But it doesn't mean that we won't join the reconciliation roadmap. That's the resolution we have made by consensus and we will definitely take part," he said from the stage at their barricaded encampment in central Bangkok.
"But the reconciliation plan is very vague and Abhisit's promise is slippery. We have to make sure what we are getting before we declare victory. We do not trust the Democrats and Abhisit."
Abhisit has said his plan takes into account the protesters' main grievances, and includes respect for the monarchy, reforms to resolve economic injustice, free but responsible media to be overseen by an independent watchdog agency, independent investigations of violent incidents connected with the protests, and amendment of the constitution to be fairer to all political parties.
|Red shirts want details of the plan saying they do not trust the government [GALLO/GETTY]
The political standoff that has gone on for nearly two months has been long and bitter, marred by outbreaks of violence that left 27 dead and more than 1,000 injured last month.
A state of emergency has been in force in Bangkok since April 7 and thousands of troops and riot police surround the red shirts encampment, out of sight most of the time or lounging around in small groups.
Financial markets were shut on Wednesday for Coronation Day and there was no movement on the political front, with neither side wanting to be seen as disrespectful to Thailand's revered king.
But Sukit Udomsirikul, a senior analyst at Siam City Securities, said stocks were bound to slip back on Thursday, especially with added pressure on world markets from the euro zone's debt problems.
"Yes, protesters have agreed to enter into a reconciliation process but crucially, they're still not leaving the protest site and demand a date for dissolving parliament," Sukit said.
"On the whole, tensions are cooling and the chance of another major blow-up should recede now that both sides are talking about reconciliation."