Jongjet Aoajenpong, the director of Police hospital, was quoted by the AFP news agency as saying that an Italian journalist was shot in the stomach and "died before arriving at the hospital".
Red shirts divided
Al Jazeera's Aela Callan, also reporting from Bangkok, said women and children were still in the 3-sq-km protest area.
But the area in front of the stage appeared to be thinning out, she said, and protesters and leaders appeared divided: some seemed to want to fight the troops but others were just sitting on the ground, waiting to see what would happen.
There were also reports that at least one of the red shirt leaders had fled the scene but they could not be immediately confirmed.
About 100 soldiers armed with automatic rifles and shotguns, along with several machine gun mounted armoured personnel carriers, breached the red shirts' barricade at the southern end of their protest site on Wednesday.
The armoured vehicles had repeatedly rammed the barricade made up largely of tyres, sharpened bamboo poles and razor wire before breaking through the flattened structure.
Troops and red shirts had been periodically exchanging gunfire before the soldiers broke through the barricade.
The military appeared to be moving slowly in their operation, and it was possible that they were leaving the north relatively open for red shirts to leave their encampment.
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.
Guerrilla war warning
|Protesters lit fuel-soaked tyre barricades but the army countered with water canon [AFP]
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.
And Thaksin Shinawatra, the ousted Thai prime minister whom many of the red shirts support, said on Wednesday that he feared a military crackdown could lead to guerrilla warfare across the country.
"There is a theory saying a military crackdown can spread resentment and these resentful people will become guerrillas," Thaksin told the Reuters news agency by telephone.
Government claims success
The government said hours after launching the offensive on Wednesday that the "security operation ... has been successful".
Panitan Wattanayagorn, a government spokesman, also said on television that protest leaders had fled the area, and called on citizens to report protest leaders if they were spotted outside the camp.
But one of the protest leaders, Nattawut Saikua, appeared on stage in the protest zone several minutes before Panitan spoke and said he had not fled.
|Gunfire has been heard throughout the hours-long military operation [EPA]
The government offered safe passage to unarmed, civilian protesters after moving into the protest camp and said buses were waiting to send them home.
Soldiers were heard shouting that protesters' lives were in danger if they did not surrender.
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.
Wednesday's military operation comes after the government rejected holding further negotiations with the red shirts until they left their rally site.
A mediation proposal, floated by a group of 64 senators in the 150-member upper house on Tuesday, was accepted by the protesters but rejected by Abhisit Vejjajiva, the prime minister.
Satit Wonghnongtaey, a government minister, said while Abhisit welcomed negotiations, the government insisted "talks will happen only after the protest has ended".
The crisis, which began when demonstrations were launched in mid-March, has now left around 70 people dead and about 1,700 wounded.