However, he also stated he would not order a crackdown on the red shirts, leading to criticism from some sides that he was showing weakness in handling the protests which have now lasted for almost four weeks.
The issuing of the arrest warrants came after hundreds of red shirt protesters briefly stormed the Thai parliament earlier this week, forcing MPs to flee the building, some by military helicopter.
Asked about the charges that formed the basis for the warrants, Lieutenant General Thangai Prasjaksatru, commander of Thailand'sCentral Investigation Bureau, told the AFP news agency that red shirt leaders had "breached a state of emergency and shut down" Bangkok's commercial hub.
No arrests have so far been reported.
On Thursday, the government also shut down an opposition TV station and dozens of websites, in a bid to control escalating anti-government rallies with censorship rather than force.
However, the protesters said on Friday they would return to the TV station that broadcasts their demonstrations to protest against the shutdown.
"We are marching now to ask them why they closed down [the] People Channel and what right they have to shut out our eyes and ears," Nattawut Saikua, a red shirt leader, told thousands of supporters in central Bangkok.
The television station is located in Pathum Thani province, north of Bangkok and was also the scene of protests on Thursday.
Al Jazeera's Aela Callan, reporting from Bangkok, said that the next 24 hours would be crucial for Abhisit's government.
"The country will be closely observing how he handles this situation, considering that he is facing mounting cricticsm and is starting to look very weak in the eyes of the Thai public if he does not put a stop to the demonstrations," she said.
"But the government does not want to be seen as firing the first shot."
|Critics are accusing Abhisit of weakness for failing to to put a stop to the red shirt rallies [AFP]
A large security presence remains in Bangkok, and according to an army spokesman, about 33,000 extra police and soldiers have been mobilised in and around the capital.
Our correspondent said the red shirt leadership is advising protesters to stay calm as the army comes in.
Abhisit has previously entered negotiations with the red shirts and ordered security forces to pull back from possible confrontations.
On Thursday, he called off a planned visit to Vietnam for a meeting of Southeast Asian leaders because of the escalating crisis, which investors fear could derail the country's high-performing economy.
The red shirt movement supports the ousted prime minister Thaksin Shinawatra, and see Abhisit, an Oxford-trained economist, as a stooge controlled by the unelected establishment and the military.
The protesters say Abhisit - who came to power in a 2008 parliamentary vote after the courts dissolved a pro-Thaksin party in government at the time - should call an election and let the people choose their government.