The BGB was joined by the army and the police in combing operations in Rangamati district. Troops were also massed on the border region of Bandarban, specially around Thanchi, where the gunbattle took place on Wednesday.
"We have got some indications about rebel casualties. Locals say they found the rebels drag away eight to 20 of their comrades, we have also seen blood trails at the spot of the encounter," Maj-Gen Aziz told journalists at BGB's Peelkhana headquarters.
He said the BGB operations started early on Thursday and the patrols managed to recover many leftovers of the rebels -- from belt to bullets.
An accomplice of the 'Arakan Army' was nabbed from Rangamati on Thursday, raising hopes of leads about the rebel movements and intentions.
The BGB chief said the Myanmar separatists might move back and forth across a hilly and forested border, but there was no chance for them to set up a base there.
He said his force tackled the situation well and fast but operations had to continue.
He also said Bangladesh and Myanmar would work together to prevent the rebels from getting to be a problem.
“We exchange information during any such operation,” he said.
Maj-Gen Aziz said the BGB patrol that was attacked on Wednesday was patrolling the area on a boat.
“The attack was swift and unexpected. We were not ready as we find the borders with India and Myanmar always calm,” he said.
The attack is believed to be a result of the seizure of 10 horses used as transport by the Arakan army on Tuesday.