In the latest influx, some 5,000 more Rohingyas entered Bangladesh through Ulubonia point of the Naf River under Teknaf upazila on Monday.
Locals said the Myanmar nationals started gathering at the no-man's land along the border since the morning. Later, they crossed the river into Bangladesh by hired boats.
Nazir Ahmed, 55, son of Abul Hossain of Jabbarpara in Bhuchidang area in Rakhine State of Myanmar, said they entered Bangladesh through the Ulubonia point after walking on foot for five days.
Meanwhile, members of Border Guard Bangladesh recovered 30,000 Yaba tablets and 80 cartons of cigarette searching the belongings of the Rohingyas who got down from boats at Shah Porir Dwip of Teknaf on Sunday night.
A patrol team of the paramilitary force recovered the contraband items around 9pm.However, no one was arrested in this connection.
Besides, Road Transport and Bridges Minister Obaidul Quader on Monday feared that drugs and firearms might be smuggled into the country by some of the fleeing Rohingyas.
Quader, also Awami League general secretary, expressed his apprehension while distributing relief materials among the Rohingyas who have taken shelter in Bangladesh amid persecution on them by the Myanmar security forces in Rakhine.
He, however, said the law enforcers have been on alert so that the Rohingyas cannot get involved in criminal activities here.
The ruling party leader also said the Rohingya crisis will be resolved through diplomatic efforts.