Teknaf 2 BGB Commander Lt Col Abujar Al Zahid said they carried out raids at four different points of the river on Monday morning.
“Each boat was carrying about 15 Rohingyas,” he told the Dhaka Tribune.
Over the past three days, the BGB has pushed back 18 boats filled with Rohingya refugees.
The Myanmar Army has been conducting counterinsurgency operations in the Rakhine state after nine policemen were killed in coordinated attacks on a number of border outposts in early October.
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More than 30,000 people, mostly Rohingyas, have been displaced since the crackdown began. Rohingya activists say more than 100 people have been killed so far.
A UN official has accused Myanmar of carrying out “ethnic cleansing” of the Rohingya Muslims.
John McKissick, head of UNHCR in Cox's Bazar, told the BBC that the actions of the Myanmar troops were forcing people to cross the river into Bangladesh.
"(They are) killing men, shooting them, slaughtering children, raping women, burning and looting houses," he said.
The Myanmar government and army deny allegations of atrocities.
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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 on the Rohingya issue.