They also gained entry to the grounds of Government House - prompting the prime minister to move his weekly cabinet meeting to military headquarters elsewhere in the capital.
Protesters - many clad in yellow as a mark of loyalty to Thailand's revered King Bhumibol Adulyadej - are now said to have concentrated in the grounds of Government House.
"We are now in Government House and won't move until the government resigns," said PAD leader Sondhi Limthongkul.
Thousands of police officers have been deployed around the protests.
Anti-government protesters storm the state TV station and surround government offices
'I will stay'
Protesters ignored a police deadline of 1800 local time (1100GMT) to clear the area.
But the government says it will not use violence against them - saying that instead it would seek a court order to arrest PAD leaders.
The police and government say some 85 people have already been arrested. Thai TV has shown knives and a handgun purportedly seized from protesters.
Mr Samak, who was elected last December, accused the protesters of trying to provoke the military to stage a coup.
"I will not resign, I will stay to protect this country," he said.
He said police surround the protesters, allowing people to leave but not allowing people or supplies in.
"I ask all the protesters who have been blockading or occupying government offices that you still have a chance to withdraw and go back to your homes," he said.
Meanwhile, in a TV interview, army chief Anupong Paochinda insisted there would be no coup attempt.
Thailand's stock market fell up to 2.5% amid the instability.
This is a mass protest movement with a difference, according to the BBC correspondent in Bangkok, Jonathan Head.
Despite the name, the People's Alliance for Democracy is actually campaigning for an end to democracy, our correspondent says.
It wants a largely appointed parliament, and a legalised role for the military as a kind of referee in Thai politics, he adds.
The PAD has already played a central role in Thai politics, beginning three years ago as a movement to bring down Thaksin Shinawatra, then the most powerful elected leader Thailand had ever known.
Its protests set the stage for the coup that ousted him in 2006, and probably helped ensure the legal cases against him went ahead this year, resulting in Mr Thaksin and his wife going back into exile.
Mr Samak is still defiant. His government has a clear majority in parliament, and he insists he retains a democratic mandate from last December's election.
But he seems unable to shake off this determined and apparently well-funded opposition movement, our correspondent adds.
He has also been unable to persuade the security forces to control the protests, raising suspicions that the PAD must have some powerful backers inside the armed forces or among the royalist elite.
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