The BGB personnel intercepted the trespassers at different points of the Naf River early Saturday morning.
“They tried to enter Bangladeshi territory via the Hnila Fulerdeil point between 5am and 7am, but the BGB patrol teams sent them back,” said Lt Col Abujar Al Zahid, commander of BGB's Teknaf 2 battalion.
Each boat was carrying 10-15 Rohingyas, the BGB commander told the Dhaka Tribune.
Hundreds of Rohingya Muslims have been trying to illegally enter Bangladesh after Myanmar troops launched a crackdown in the Rakhine state in response to attacks on three border posts on October 9 that killed nine police officers.
Bangladesh has stepped up security along its border with Myanmar to prevent influx of Rohingyas fleeing the violence in Rakhine which has killed at least 86 people and displaced 30,000 others.
Myanmar and the military have denied accusations by fleeing Rohingyas and rights groups of raping women, torching houses and killing civilians during their operations.
Myanmar does not recognise the Rohingyas as its citizens and dubs them “Bangali”. Rohingyas who have managed to enter Bangladesh have taken shelter at refugee camps and other places in Cox’s Bazar.
Bangladesh has so far pushed back thousands of Rohingyas.
The latest violence is the most serious since the 2012 communal clashes. Many have criticised Nobel Peace Prize winner Aung San Suu Kyi for her silence regarding the military persecution of Rohingyas, although her party is in power.