But overnight numbers dwindled to less than 1,000, a police official told AFP news agency.
The so-called "Red Shirt" protesters have campaigned against the government since a court order ousted the previous government made up of Thaksin allies.
Protest leaders have said they will stay outside Government House for at least three days.
Aside from dissolving parliament, the "Red Shirts" also want the government to prosecute leaders of the rival "Yellow Shirts", whose protests closed down Bangkok's two main airports 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.
The protests are 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.