Many of the demonstrators, who had earlier faced-off against the troops across an intersection, also pulled back on Monday.
'Enforce the law'
Al Jazeera's Wayne Hay, reporting from Bangkok, said the red shirts had announced that they would hold a big rally on Tuesday and could possibly move around the city from their base in the main Rachaprasong shopping area.
They had intended to set up another protest site in the financial district, much like their main encampment in the commercial centre.
The red shirts later said they would not take to Silom Road, our correspondent said, but there was still the possibility they would make good on their threat to fan out across the city again to once again raise the level of protest to put more pressure on the government to resign.
There were signs, however, that the military was taking the red shirts seriously, our correspondent said, and government forces said the protesters would not be allowed to move around the city.
Colonel Sansern Kaewkamnerd, a spokesman for the army, said the troops "won't let [protesters] go anywhere further".
He stopped short of using the word "crackdown" but said: "We will not allow people to hurt police officers, soldiers or civilians again - or to seize military vehicles or weapons."
He added that protesters occupying an upscale shopping and hotel district nearby would be dealt with.
"Let's say that we are left with no choice but to enforce the law," Sansern told TNN television.
"Those who do wrong will get their punishment. Taking back the area along with other measures are all included in enforcing the law. All this must be done."
Sansern said security forces would be sent to secure high-rises around the demonstration area to prevent the "third hand" from launching attacks.
At least 25 people were killed, including senior military officers, and more than 800 people were wounded, including about 300 soldiers, in clashes between troops and demonstrators on April 10, the first outbreak of violence in the six-week long protests.
The government accuses "terrorists" or the "third hand" - unknown provocateurs - armed with guns and other weapons of orchestrating the violence and says weapons were stolen from the military.
Yellow shirts' warning
Adding to concerns about further unrest, leaders of the so-called "yellow shirt" movement said on Sunday that they would take action themselves and hold a mass rally unless the government "strictly and efficiently enforces the law" to deal with the crisis.
|The red shirts say their ranks are growing despite attempts to block them [EPA]
The yellow shirts, representing royalists, the business elite, aristocrats and urban middle class and led by People's Alliance for Democracy (Pad), are opposed to Thaksin Shinawatra, the ousted prime minister whom many of the red shirts support.
They would not reveal their exact plans should the authorities fail to clear the streets of the red shirts, our correspondent said, but they did not rule out direct confrontation with the Thaksin supporters who have occupied Thailand's streets since March 12.
The yellow shirts staged a crippling eight-day blockade of Bangkok's airports in December 2008, which left more than 230,000 tourists stranded, disrupted trade and led to credit rating downgrades for Southeast Asia's second-largest economy.
The siege ended when the then ruling party, aligned with Thaksin, was dissolved for electoral fraud, paving the way for Abhisit Vejjajiva to become prime minister after a parliamentary vote the red shirts say was influenced heavily by the military in a "silent coup".
The red shirts, formally known as the United Front for Democracy against Dictatorship, want Abhisit to step down, dissolve parliament and call new elections.
But the prime minister has rejected claims that his government is illegitimate and has refused to step down.
Abhisit failed to deliver his regular televised address on Sunday for a second week and has been uncharacteristically reclusive since last week's clashes.
The red shirts were initially camped in a historic district of Bangkok, and it was a failed attempt by security forces on April 10 to flush them from that neighbourhood that led to the worst political violence Thailand has seen in 18 years.
|Troops have barricaded the headquarters of the Bangkok Bank with barbed wire [Reuters]
Since then, there has been an uneasy calm, with few troops on the streets and the protesters consolidating at their "final battleground" in Bangkok's main shopping area in Rachaprasong.
The protests have scared off tourists and rattled the stock market, and in another blow to the vital tourism sector, which accounts for six per cent of the economy, the military declared the main shopping area unsafe on Sunday.
Sansern said military checkpoints were being set up at entry points to the capital and within Bangkok to try to prevent more protesters from reaching the main rally site.
"The protest area is unsafe. Authorities need to control it by sending security personnel into the surrounding high-rise buildings," Sansern told a news conference.
He said soldiers would help "prevent people with ill intentions from infiltrating the area".
But Jatuporn Prompan, one of the red shirt leaders, said on Sunday that "the authorities have always tried to block people from joining us, but still we are getting more people".
The seemingly intractable crisis has fuelled speculation that, with the government and security forces in disarray and concerns about clashes between rival demonstrators, hardliners within the military may decide to stage a coup to end the impasse, a move analysts say would likely backfire.