Earlier in the morning, troops used loudspeakers to tell protesters at the protest site in Bangkok's high-end Rachaprasong shopping district to go home, saying their lives were in danger, our correspondent said.
Bracing for battle
Al Jazeera's Aela Callan, also reporting from Bangkok, said a few protesters could be seen leaving, but the bulk of the estimated 3,000 appeared to be staying put and appeared to be bracing themselves for battle.
Sean Boonpracong, a red shirt spokesman speaking to Al Jazeera from Bangkok, warned that if the troops entered the protest site, "this will be a second Tiananmen Square", referring to China's deadly crackdown on demonstrators in 1989.
"You will see the biggest massacre ever aired on television," he said.
The authorities had warned the red shirts to leave their protest site by 3pm (08:00 GMT) on Monday, saying that those who remained faced two years in prison.
However, the protesters defied the order and the deadline passed without any action being taken.
The troop build-up comes after the government rejected holding further negotiations with the red shirts until they left their rally site.
Satit Wonghnongtaey, a government minister, said on Tuesday that the prime minister, Abhisit Vejjajiva, had welcomed negotiations but insisted that "talks will happen only after the protest has ended".
Jatuporn Prompan, another red shirt leader, said "as long as the troops are confronting the people, the people will fight".
A mediation proposal, accepted by the protesters but subsequently rejected by Abhisit, was floated by a group of 64 senators in the 150-member upper house on Tuesday.
Robert Amsterdam, Thaksin's lawyer, speaks
to Al Jazeera about the Thai crisis
As the prospects for official talks unravelled, fighting erupted again in the Din Daeng district on Tuesday, the latest in a series of clashes since Thursday that has left at least 38 dead and hundreds injured.
The United Nations has called on both sides to "step back from the brink", with Navi Pillay, the high commissioner for human rights, saying there was a high risk things could "spiral out of control".
"To prevent further loss of life, I appeal to the protesters to step back from the brink, and the security forces to exercise maximum restraint in line with the instructions given by the government," she said in a statement.
The crisis, which began when rolling demonstrations were launched in mid-March, has now left nearly 70 people dead and about 1,700 wounded.