The military has also declared certain areas of Bangkok to be "live fire zones", which means security forces will use live ammunition against protesters trying to enter these areas.
Al Jazeera's Wayne Hay, reporting from the city, said the army's operations were aimed to seal off the protest site in an attempt to apply pressure on the red shirts.
However, the army gave warning that it would move against the demonstrators' main rally site unless they dispersed, although it gave no timetable for any such action.
"There is a plan to crack down on Ratchaprasong if the protest does not end," Sunsern Kaewkumnerd, an army spokesman, told AFP news agency.
"But authorities will not set a deadline because without effective planning there will be more loss of life."
Scenes of urban warfare erupted on the southern and northern fringes of the red shirts' encampment in the heart of Bangkok, after the army moved in on Thursday to seal off the area.
Abhisit, who last week overturned a plan to hold early elections, warned that the government "cannot turn back" in the two-month standoff.
He said that he was attempting to quell violence with minimum bloodshed.
In a televised address on Saturday, Abhisit said his government was trying to "restore normalcy with minimal loss" to the capital.
But the protesters, seeking his resignation and early elections, seemed to be in no mood to capitulate.
As soldiers opened fire on demonstrators, they responded with sporadic attacks on the army's positions, using petrol bombs to torch vehicles, and attempting to barricade their camp with piles of burning tyres.
More than 50 people have been killed and 1,600 wounded since the protests began on March 12, according to figures from the emergency services and the public health ministry.
"The current situation is almost full civil war," Jatuporn Prompan, a protest leader, said.
"I am not sure how this conflict will end."
Daily life disrupted
For two months, thousands of protesters have turned a large area of Bangkok into a virtual city within a city, crippling a retail and hotel district and disrupting daily life for residents in the city of 12 million people.
The rally site, where demonstrators sleep on mats on the ground and listen to speeches and music blasted from giant speakers, stretches for several square kilometres.
Al Jazeera's Wayne Hay reports on the continued standoff on the streets of Bangkok
It is fortified with razor wire, bamboo sticks and piles of tyres.
The face-off capped weeks of political turmoil in Thailand with the red shirts - predominantly supporters of ousted prime minister Thaksin Shinawatra - converging on Bangkok to press for the current government's resignation.
Abhisit had offered to call new elections if red shirts ended their two-month protest, but the demonstrators have insisted that the country's deputy prime minister must first be charged for the deaths of 25 red shirt supporters.
The mostly poor and working-class red shirts say the government is elitist and undemocratic because it came to power in a 2008 parliamentary vote after a court ruling ousted elected allies of Thaksin.
Protest leaders have also called for the intervention of Thailand's revered King Bhumibol Adulyadej.
But the monarch, seen as a unifying force, has been hospitalised since September and has avoided commenting directly in public on the crisis.