Emergency services reported that at least 20 soldiers had been injured in one blast, and separately a grenade exploded near to the office of Abhisit Vejjajiva, the prime minister, but there were no initial reports of injuries.
Wayne Hay, Al Jazeera's correspondent in Bangkok, said: "We witnessed a fierce battle between the red shirts and the military at Democracy Square.
"The red shirts were very much in control of that area there, with a bit of a party scene developing as we left the area.
"The military has pulled well away, with the red shirts having won control of their vehicles, tanks and armoured personnel carriers. So this was very much a victory for the red shirts when the army announced they were pulling back.
"The concern for the governent is that some of the soldiers and police may well side with the red shirts. So even if they had the orders to push hard against the red shirts, they may not do so."
As violence raged on the streets of Bangkok, Veera Musikapong, a leader of the red shirts, said: "We are changing our demand from dissolving parliament in 15 days to dissolving parliament immediately.
"And we call for Abhisit to leave the country immediately."
Speaking to Al Jazeera on Saturday evening, Sean Boonpracong, a red shirts spokesman, said: "We are 100 per cent on a war path, with bare hands, against the army."
|Al Jazeera's Wayne Hay reports on the heightening violence in Bangkok on Saturday
But Abhisit, who has been holed up at an army barracks, said that he would not step down after the day of clashes.
"I and my government will continue to work to resolve the situation," he said in a televised address to the nation on Saturday, rejecting calls from the red shirts to hold immediate elections.
"The military has stopped the operation, while protesters have retreated to the rally site."
Abhisit also said that the military was only using live rounds in "self-defence".
"I would like to say that the use of live bullets is only allowed in cases of firing into the air and in self-defence," he said.
Abhisit expressed "regret" to the families of the victims and said an investigation would be launched.
Hiro Muramoto, a Japanese national working for the Reuters news agency, was shot in the chest and died before reaching Klang hospital, Pichaya Nakwatchara, the hospital's director, said.
Several thousand red shirts swarmed around Bangkok's main shopping district on Saturday morning, a stretch of upscale shopping plazas and five-star hotels that has been held in a carnival-like atmosphere for a week by the red shirts.
Protesters used taxis and pickup vans to barricade themselves in the area, and expanded their control to include several more blocks, after riot police, who massed at the scene, retreated after being surrounding by the red shirts.
Troops then mounted two major offensives on protesters in the Phan Fah bridge and Rajdumnoen Road area in the morning. Both times they fired rubber bullets and tear gas but failed to clear the area.
An afternoon offensive ended in a tense standoff with many people wounded. As night fell, troops opened fire again with rubber bullets about 500 metres away at an intersection leading to the popular tourist area, Khao San Road.
Shop and car windows on Khao San Road were shattered as many people lay wounded on the street.
The violence comes exactly a year after about 10,000 of the supporters of Thaksin Shinawatra, the former prime minister removed from power, brought traffic in Bangkok to a standstill for several days, occupying major intersections.
The red shirts say Abhisit lacks a popular mandate after coming to power in a 2008 parliamentary vote following a court ruling that dissolved a pro-Thaksin ruling party.
They want immediate elections that Thaksin's allies would be well placed to win.