The so-called Red Shirt anti-government protesters placed gas canisters just outside a bus, set the vehicle on fire and retreated slightly before trying to regain ground.
The two sides were locked in a standoff and tensions remained high, our correspondent said.
In his address, Abhisit said the state of emergency declared on Sunday was only to restore calm and would remain for now.
He said that troops would only use force in self defence and warned that protesters had seized three cooking gas trucks and were threatening to blow them up.
Our correspondent said that while protesters had placed several cooking gas canisters in the middle of the road in an effort to keep troops at bay, he had not seen any gas trucks at the scene.
Hours earlier, at the the same intersection, shots were fired and petrol bombs and stones hurled as soldiers and demonstrators clashed.
Peeraphong Saicheau, the director of the Bangkok Medical Centre, said 77 people had been injured, with 19 admitted to hospitals.
Four people had gunshot wounds - two civilians and two soldiers – he said.
An army spokesman said that soldiers, who were trying to clear the intersection, were shot at by protesters before dawn and had fired back.
Colonel Sansern Kaewkamnerd told local radio that troops would "start with soft measures and proceed to harder ones", but added: "We will avoid loss of life as instructed by the government."
Sean Boonpracong, the international spokesman for the United Front for Democracy Against Dictatorship, the group that has been leading the Red Shirts' protest, criticised the military's "aggressive tactics ... shooting at unarmed civilians".
"If things get any worse, there will be more blood and the government will be responsible"
Sean Boonpracong, United Front for Democracy Against Dictatorship
But he admitted to Al Jazeera that "some of us have to fire back in defence with handguns".
The spokesman demanded the army to stop its operations immediately and that Abhisit resign, dissolve parliament and call fresh elections.
"If things get any worse, there will be more blood and the government will be responsible," he said, adding that if the army started shooting at protesters, they may occupy Government House for their "safety".
Panitan Wattanayagorn, a spokesman for the government, said troops had successfully cleared the busy intersection near the capital's Victory Monument landmark where about 100,000 people had gathered late last week to demand Abhisit's resignation.
"The operation is complete, and a number of protesters have been detained in safe places. The operation is in line with the law, accountable and reasonable," Panitan said on national television, soon after the military crackdown.
But our correspondent said protesters had returned to the intersection hours afterwards.
'No martial law'
Panitan told Al Jazeera that Abhisit had "delegated power in terms of operations" to a committee led by several military officers who were "handling the emergency situation".
But he said that the prime minister remained in charge of the country and that there was "no martial law".
He also said that the military had been given live ammunition but were "under strict orders not to aim at the people or not to shoot at the people".
Keen to show that he still commanded the loyalty of the armed forces and the police, Abhisit appeared on television in the early hours of Monday, flanked by commanders of the army, navy, air force and the deputy police chief.
"I can confirm that the government and security agencies are still unified. You can see all the heads of the armed forces meeting with me right now," he said.
But the loyalty of the police force has been questioned after some policemen were seen putting on red shirts and joining protest rallies
Thailand has seen weeks of protests by the Red Shirts, who support Thaksin Shinawatra, the prime minister ousted in a military coup in 2006.
Thaksin, who continues to wield considerable political influence in the country, despite being in exile since September 2006, called on Sunday for his supporters to overthrow the government, promising to return if the government moved to crack down on protests.
|Medics say at least four of the wounded
had gunshot injuries [AFP]
T Kumar, the Asia and Pacific director at Amnesty International USA, told Al Jazeera that the military's action against Thaksin supporters on Monday contrasted sharply against its inaction against anti-Thaksin demonstrators who held protests last year against two successive governments filled with Thaksin allies.
"It was a very calculated move to support the current government, which the military did not do when the current prime minister was in the opposition," he said.
Those protests eventually led to court rulings that deposed the pro-Thaksin governments and ushered in Abhisit's government.
"The best way to control this situation is to have an election at this moment," he said, warning that if Thailand's Southeast Asian neighbours and the international community did not press the government to hold elections, the country would "go downhill", Kumar said.