Muslim student groups in Bangkok are being closely monitored by Thai police intelligence.
"It is possible that the insurgents will expand their attacks to Bangkok, because we have learned of their movements in various universities where they conceal themselves in the uniforms of students," Boonrawd said.
He said he had ordered the military in Bangkok to "take the utmost precaution" during a major Buddhist holiday, Makha Bucha, on March 3.
Surayud Chulanont, Thailand's prime minister, said on Thursday the possible insurgent strikes in Bangkok were still "speculation".
He has pledged to stick to a plan to hold talks with separatists in the nation's Muslim-majority south despite the upsurge in deadly violence.
"I think before the end of my government, I think we can make some progress in terms of trying to calm down the violence and initiate some talks" with "terrorists who are trying to create violence in the south," he said.
The separatist insurgency has been largely confined to three Muslim-dominated provinces in southern Thailand bordering Malaysia, where more than 2,000 people have died since early 2004.
"If they want to solve the problem, they should come and talk. That's the best way"
Surayud Chulanont, Thai prime minister
Since taking office after a bloodless military coup in September, Surayud has apologised to Muslims for past abuses, offered to hold talks with insurgents and proposed a special economic zone in the south, one of Thailand's poorest regions.
The prime minister said his government was ready for peace talks, but acknowledged that there could be no quick fix to the three-year insurgency.
"I think it will not be very easy to stop all this violence within a four-month period. It will take a long time, trying to convince people that this is not the correct way to solve the problem," he said.
"If they want to solve the problem, they should come and talk. That's the best way."
Surayud and his Malaysian counterpart, Abdullah Ahmad Badawi, recently agreed to boost their cooperation in quelling the violence, with Kuala Lumpur helping to facilitate talks with insurgents.
But Surayud's efforts to launch peace talks are likely to face obstacles, largely because no one knows who the militants are.
Peace talk plans may hit a wall as no-one
knows who the insurgents are [AFP]
The shadowy insurgents never claim responsibility for attacks, and have made no public demands.
Early this week, a coordinated rebel assault, including bombings, arson and shootings, killed eight people and wounded nearly 70 on Sunday and Monday.
The attacks were the first to occur simultaneously in all four southern provinces - Yala, Narathiwat, Pattani and Songkhla - where the rebels operate.
Other violence linked to the Muslim separatist insurgency included three fatal shootings on Tuesday and Wednesday, police said.
On Wednesday, Wiriya Chawakul, confidante to Thailand's Queen Sirikit, narrowly escaped death when the vehicle she was travelling in was ambushed by suspected Muslim insurgents, police said.
The attack came just a few hours after other suspected insurgents set fire to a large warehouse for rubber, the south's main commodity.
The restive south has had a history of separatist violence ever since mainly Buddhist Thailand annexed what was an autonomous ethnic Malay sultanate a century ago.
Muslims account for five per cent of Thailand's 65 million mainly Buddhist population.