Flag-waving protesters who have vowed to topple the Thai prime minister took to the streets of Bangkok for a fourth day, declaring they would take over "every ministry" of the government.

The brash threat was the boldest challenge yet to Yingluck Shinawatra's embattled administration.

But the demonstrators appeared to number only in the tens of thousands - far less than the 100,000-plus present when they began Sunday.

The numbers indicate they are unlikely to bring down the government on their own without more popular support or judicial or military intervention.

By late yesterday afternoon demonstrators had massed inside or around at least six of the government's 19 ministries as well as a sprawling government complex which houses the Department of Special Investigations - the country's equivalent of the FBI.

Late on Tuesday police issued an arrest warrant for Suthep Thaugsuban, the former deputy premier who leads the protest movement after being ousted from office in 2011.

He camped out overnight at the Finance Ministry, which has been converted into an ad-hoc protest headquarters.

But there appeared to be no attempt to detain Mr Suthep as he led some 6,000 supporters out of the Finance Ministry early yesterday.

The crowd eventually grew to 10,000, while thousands more marched from another base at the city's Democracy Monument and other smaller groups gathered elsewhere, waving Thai flags.

The undemocratic aspirations of Mr Suthep became clear on Tuesday night when he announced for the first time that he wanted replace the government with a non-elected council.