The announcement came after the army overran their heavily barricaded encampment in central Bangkok on Wednesday.
Seven Red Shirt leaders went on stage in the core protest zone to announce their decision, which was greeted with shouts of dismay from the men and women gathered around.
Protest leader Natawut Saikua said "we have done our best." Weng Tojirakarn said "we want to prevent further losses of our Red Shirt brothers and sisters."
He said "let us first prevent further losses of lives," and urged supporters to leave the area.
Thai soldiers with armored vehicles stormed into a fortified encampment occupied by anti-government protesters Wednesday, breaking through bamboo-and-tire barricades in a major military offensive in the heart of Bangkok.
At least two protesters were killed and one foreign journalist appeared dead after getting shot in the chest. Two other foreign journalists were wounded by bullets.
Surreal scenes of warfare erupted in one of the ritziest parts of the capital, as troops armed with M-16s marched through the central business district past upscale apartment buildings to retake the area around manicured Lumpini Park, which has been under the control of protesters camped there for weeks.
Government spokesman Panitan Wattanayagorn declared the first stage of the army operation to secure the area around Lumpini Park successful and said that some protest leaders had fled. He asked the public to inform police if any of the leaders were spotted.
However, two of the three key leaders remained in the protest zone giving defiant speeches and singing on a stage, as troops drew closer.
An Associated Press reporter who followed the troops into the protest camp saw the bodies of two men sprawled on the ground, one with a head wound and other apparently shot in the upper body. They were the first known casualties in the assault that began before dawn Wednesday on a 1-square kilometer (3-square kilometer) stretch of downtown Bangkok that protesters have occupied.
Troops fired M-16 rifles at fleeing protesters and shouted, "Come out and surrender or we'll kill you."
An AP photographer saw three foreign journalists shot. One was an Italian photographer shot in the chest. His eyes were rolled back and he showed no signs of life. A Dutch journalist walked into the hospital with a bullet wound in his shoulder. The third journalist was a 53-year-old American documentary filmmaker who was treated for a shot in the leg.
The photographer also saw at least seven Thais brought to a hospital. It was unknown if they were dead or unconscious.
As troops entered the fringes of the protest area, they passed smoldering fires and hastily abandoned campsites where clothes were still hanging on laundry lines. Shoes were scattered, chairs were overturned and a huge pile of rice was covered with flies.
Panitan went on national television four hours after the crackdown began to announce it was under way, speaking first in Thai and then in English.
"The operations will continue throughout the day," Panitan said. "We would like to reassure the citizens of Bangkok that the operations are designed to make sure we stabilize the area."
The army action came after weeks of defiance by the protesters who are seeking to oust the government of Prime Minister Abhisit Vejjajiva.
"This is D-Day," said one soldier when asked earlier in the day if this was the final push to clear the protest zone.
Thick black smoke from mountains of burning tires darkened the skies Wednesday, billowing over the skyscrapers of this Asian metropolis of 10 million that has descended into chaos over the last week, with at least 39 killed, most of them civilians.
The violence in Bangkok, a popular stop for tourists heading to Thailand's world-famous beaches, has caused concern internationally and raised doubts about the stability of this Southeast Asian nation.
The so-called Red Shirt demonstrators marched into Bangkok in mid-March to demand the resignation of Prime Minister Abhisit Vejjajiva, dissolution of Parliament and immediate elections.
They created an encampment in Bangkok's posh downtown Rajprasong district in April, surrounding themselves by a barricade of tires and bamboo spears, some of which appeared to be in flames Wednesday.
An estimated 3,000 people were believed to be inside the 1-square-mile (3-square-kilometer) protest zone, which has taken over several blocks of downtown Bangkok's toniest shopping and tourism district.