One or two small groups within the BRN which disagree with the peace process have continued to engage in subversive activities to try to stop the talks, Lt Gen Paradorn said.
He was speaking after suspected insurgents spray-painted a message in red on the concrete path near the gate of Thetsaban 3 School in Narathiwat's Sungai Kolok district on Sunday.
The message "SUN RKK BAK", indicating Runda Kumpulan Kecil (RKK) separatists may have returned to the region, has heightened concerns over the safety of teachers in the province.
Lt Gen Paradorn said he believed the message was from members of the RKK guerrilla group.
The spray-painted message reflected how some groups within the BRN disagreed with the peace talks between the separatist movement and the government, said Deputy Prime Minister Pracha Promnok, who oversees national security.
The peace talks have been effectively deadlocked as the government has not agreed to the BRN's demands.
The demands include the release of detained insurgent suspects and revocation of arrest warrants for those still at large, and the state's recognition of the BRN as a liberation movement rather than a separatist group.
Lt Gen Paradorn said security agencies had sought written clarification from the BRN on precisely what they want.
The agencies also want to know what will happen if the demands are met, he said.
He said the next round of peace talks would be arranged once this clarification was received.
Lt Gen Paradorn said the government insists on continuing the talks with the BRN, hoping it would communicate with smaller groups and persuade them to support the peace process and stop the violence.
Meanwhile, a policeman was injured in a drive-by attack while driving home from Lam Mai Police Station in Yala late on Sunday night.
Pol Sgt Aphisit Ana, 21, was shot by one of two unidentified men who followed his pickup truck on a motorcycle.
Police believe the suspects are members of an insurgent group.