They plan to send groups to a range of other ministries and government offices around the capital Wednesday, said Akanat Promphan, a spokesman for the protesters.
Their objectives include the public health, labor, industry, social development and science ministries, as well as a government complex that houses multiple agencies, notably the Department of Special Investigation.
The number of demonstrators, led by the opposition Democrat Party, has declined from the huge gathering of roughly 100,000 people that assembled in Bangkok on Sunday.
Akanat said the protesters believe their current numbers to be in the tens of thousands, perhaps as many as 50,000. But authorities estimate the number of demonstrators to be 10,000, said Lt. Gen. Paradon Patthanathabut of the National Security Council.
Certain sections of some roads in Bangkok have been shut down because of the number of protesters camping out and spilling into the street, Paradon said.
Amid the tensions on the streets, Prime Minister Yingluck Shinawatra faces a no-confidence motion in parliament put forward by the opposition as it tries to unseat the government through legal means.
A vote is currently scheduled for Thursday, but the opposition`s chances of success appear slim, as Yingluck`s party has a majority.
Protesters are calling for an end to the government of Yingluck, sister of former premier Thaksin Shinawatra, the telecommunications tycoon who was ousted in a 2006 coup.
Critics of the Thai prime minister accuse her of being a puppet of her older brother Thaksin, a deeply polarizing figure who was removed from power by the military while in New York in 2006. He has since lived in exile, except for a brief return in 2008, and was convicted by Thai courts for corruption and sentenced in absentia to two years in prison later that year.
More than three weeks of anti-government protests led by the Democrat Party rose to a crescendo with the big demonstration Sunday. The protesters have since taken their rallies directly to government offices, TV networks and military installations.
At various points during the past few days, demonstrators have surrounded the foreign ministry, as well as the agriculture and interior ministries.
Yingluck has said authorities will "absolutely not use violence" to disperse the demonstrators. But the situation is delicate after Thai police issued an arrest warrant against protest leader Suthep Thaugsuban.
Paradon of the National Security Council said Wednesday that authorities are "sticking with negotiation" and trying to persuade Suthep to hand himself in.
Authorities have extended the areas around Bangkok where police are enforcing an internal security law that restricts gatherings by demonstrators.
The current protests have reanimated the tensions along Thailand`s political fault lines -- Thaksin Shinawatra`s mostly rural support base on one side, the Bangkok-based elite and middle classes on the other. The same division left the country wracked with turbulence for four years after the 2006 coup, culminating in a 2010 army crackdown on Thaksin supporters that left more than 90 dead.
The current protests are in response to a government-backed amnesty bill that could have extended a pardon to Thaksin Shinawatra and opened the door for his return to Thailand.
The Thai senate rejected the amnesty bill on November 11, but demonstrations continued, with the opposition calling for the current government to be replaced by a new administration.
More than a dozen countries have issued travel warnings for citizens to avoid areas near protests in Bangkok.