The military spokesman added that "all kinds of infrastructure, including buses and trains, waterway services, will be blocked" and that some Bangkok residents could be affected by the blockade.
A spokesman for the red shirts said they have enough supplies to last for some time. And he said protesters had no intention of dispersing, even if the government used force.
"We have decided that we have to go through with it," Sean Boonpracong told Al Jazeera's Aela Callan. "We are committed. If the troops come in, we are going to have to fight."
But protesters said they would not end their siege of the high-end shopping district in downtown Bangkok, despite the threat.
"Whatever measure you use, we are not scared," Weng Tojirakarn, a leader of the red shirts, formally known as the United Front for Democracy against Dictatorship, told the Reuters news agency.
Thousands of protesters remained at their fortified camp on Wednesday and showed no signs of leaving.
Abhisit had offered an election on November 14 - just over a year before one is due - to try to end a movement that began in mid-March with a demand for an immediate poll.
The protesters, many supporters of Thaksin Shinawatra, the former prime minister ousted in a 2006 coup, accepted the election date but are now pushing other demands.
In particular, they want Suthep Thaugsuban, the deputy prime minister, to be charged in connection with a bloody clash with troops on April 10 in which 25 people – soldiers and civilians - died.
Four other people have died in other clashes since then and more than 1,000 have been wounded.
The authorities are faced with the dilemma of how to dislodge the protesters, which count many women and children among their ranks.
"We are not going anywhere until the government shows they will take responsibility for the clash," said 39-year-old protester Panna Saengkumboon.
"People lost their eyes, their legs and arms. Others paid for this with their lives."