The southern town is due to play host to a summit of leaders from the Association of Southeast Asian Nations (Asean) leaders' meeting at the resort town of Hua Hin later this week.
Before leaving Abhisit told reporters he was confident the security forces would handle the rally peacefully.
"We will not occupy Government House but we will evaluate how long we stay outside on a daily basis"
Jatuporn Prompan, protest leader
"No, I don't worry at all," he said.
Some 3,000 police have been deployed around Government House, while another 2,000 army troops have been placed on stand-by.
Jatuporn Prompan, another protest leader, said he does not expect clashes during the protest and that demonstrations would only be in Bangkok.
"We will not occupy Government House but we will evaluate how long we stay outside on a daily basis," he told reporters, adding that protesters would not obstruct the Asean summit.
Tuesday's protest is the latest move in months of political turmoil that has swept Thailand, and threatens to further undermine confidence in an economy already reeling from the effects of the global financial crisis.
Jakrapob Penakir, a key protest leader, said the staging of the protest, just days before the Asean summit, was intended to show Thailand's regional neighbours that the present government led had no right to rule.
Abhisit was appointed prime minister in December after a court order that ousted the previous government made up of Thaksin allies.
Aside from dissolving parliament, the 'Red Shirts' also want the government to prosecute leaders of the rival "Yellow Shirts", whose protests closed down Bangkok airport late last year, and sack Kasit Piromya, the Thai foreign minister.
Piromya was a vocal supporter of the anti-Thaksin protesters, known as the People's Alliance for Democracy (PAD).
Last year hundreds of PAD supporters occupied Government House for three months, triggering a series of clashes with police during which two people were killed.
The group also seized control of Bangkok's two airports for a week in late November.