Earlier this week, Hassan Taib, the BRN liaison office chief, said in a post on YouTube that the BRN would return for talks only on two conditions - the BRN's five preliminary demands must be acknowledged and fully implemented by the "Siamese parliament", and Prime Minister Yingluck Shinawatra must place peace negotiations on the southern unrest on the national agenda.
Lt Gen Paradorn said the BRN was not happy that the Thai side had tried to bring other separatist groups into the talks, such as the Pattani United Liberation Organisation (Pulo) and the Barisan Islam Pembangunan Pattani (BIPP).
He said the Thai side can do this, because it wants to also talk to other separatist groups with different ideologies to BRN. This had been agreed on at the first round of talks, on the condition that this could be done with BRN's recognition.
"So, the talks have been postponed. Moreover, the situation in our country is not yet back to normal," Lt Gen Paradorn said.
The NSC chief had earlier said the next round of talks would probably be held in early December.
The NSC and BRN have held three rounds of talks since February, the last being in June.
Two attacks were reported in the restive southern border province of Pattani, and five people were killed.
Pol Col Yukol Prasartnanont, the Nong Chik police chief, said on Wednesday that four people were killed in a drive-by shooting in Pattani's Nong Chik district on Tuesday night.
According to investigators, seven villagers left home in a pickup truck to harvest fiddler crabs in the forest. They were attacked by four unidentified gunmen on two motorcycles. Four villagers were confrmed slain at the scene, two managed to escape and one was still missing.
Following the attack, the gunmen dragged two of bodies to the roadside and then stole the pickup truck.
A team of explosive ordnance disposal (EOD) police officers and soldiers found expended cartridge shells from M16 rifles and a 9mm handgun at the scene of the attack.
The two people who got away by fleeing into the forest told investigators that they could not contact 46-year-old Sutha Suk-ead, the missing villager.
Police were searching for Mr Sutha and also attempting to track down the four gunmen.
Another drive-by shooting took place in Pattani's Kapo district about 11pm Tuesday.
Pol Col Dulyaman Yaena, chief of Kapo police station, said Waehama Lateh, 49, a resident of Moo 7, tambon Karubee in Kapo district, was shot dead as he was walking back home along a rural road.
A gunman riding pillion on a motorbike fired at him with a handgun. Waehama took bullets in his torso and died on the spot. The killers then fled.